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Номер 12, страница 30 - гдз по алгебре 10 класс учебник Абылкасымова, Жумагулова
Авторы: Абылкасымова А. Е., Жумагулова З. А.
Тип: Учебник
Издательство: Мектеп
Год издания: 2019 - 2026
ISBN: 978-601-07-1142-6
Утверждено Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 10 классе
Глава 1. Функция, ее свойства и график. Проверь себя! - номер 12, страница 30.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1113679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb28-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1113552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Функция, ее свойства и график" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "9" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4293 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:2 [ 0 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 6997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Абылкасымова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алма" "field_patronymic" => "Есимбековна" "field_surname_rp" => null ] #original: array:12 [ "id" => 6997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Абылкасымова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алма" "field_patronymic" => "Есимбековна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 6999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумагулова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Зауре" "field_patronymic" => "Абдыкеновна" "field_surname_rp" => null ] #original: array:12 [ "id" => 6999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумагулова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Зауре" "field_patronymic" => "Абдыкеновна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Term {#1045 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null …4 ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 10 класса общественно-гуманитарного направления общеобразовательных школ" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "514" "field_priority" => "2" "field_default_folder" => "/algebra_10/Abylkasymova-u/" "field_isbn" => "978-601-07-1142-6" "field_cover" => array:1 [ 0 => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/algebra/abylkasymova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 542 "class_subject" => 387 ] ] #original: array:50 [ "id" => 4293 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 10 класса общественно-гуманитарного направления общеобразовательных школ" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "514" "field_priority" => "2" "field_default_folder" => "/algebra_10/Abylkasymova-u/" "field_isbn" => "978-601-07-1142-6" "field_cover" => array:1 [ 0 => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/10-klass/algebra/abylkasymova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} 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] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:3 [ 0 => App\Models\Element {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1291014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1101 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => 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} "task" => array:2 [ "refs" => "1113679" "type" => "task" ] "text" => "<p><strong>12.</strong> На каком рисунке изображен график функции $y = (x - 3)^2$:</p><p><strong>A)</strong> а; B) б; C) в; D) г?</p><br><strong>а)</strong><svg width="200" height="200" viewBox="-3.5 -3.5 7 7"><!-- Оси --><line x1="-3.5" y1="0" x2="3.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-3.5" x2="0" y2="3.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="3.3,0 3.1,0.08 3.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,3.3 0.08,3.1 -0.08,3.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-2" x2="-0.05" y2="-2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-1" x2="-0.05" y2="-1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><!-- Парабола y = -x^2 + 3 --><path d="M -2.5 -3.25 L -2 -1 L -1 2 L 0 3 L 1 2 L 2 -1 L 2.5 -3.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="0" cy="3" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="0.15" y="3.2" font-size="0.6">3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="3.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="3.1" font-size="0.6">y</text></svg><br><strong>б)</strong><svg width="200" height="200" viewBox="-3.5 -3.5 7 7"><!-- Оси --><line x1="-3.5" y1="0" x2="3.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-3.5" x2="0" y2="3.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="3.3,0 3.1,0.08 3.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,3.3 0.08,3.1 -0.08,3.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-2" x2="-0.05" y2="-2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-1" x2="-0.05" y2="-1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><!-- Парабола y = x^2 - 3 --><path d="M -2.5 3.25 L -2 1 L -1 -2 L 0 -3 L 1 -2 L 2 1 L 2.5 3.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="0" cy="-3" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="0.15" y="-2.8" font-size="0.6">-3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="3.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="3.1" font-size="0.6">y</text></svg><br><strong>в)</strong><svg width="200" height="200" viewBox="-0.5 -0.5 6.5 6.5"><!-- Оси --><line x1="-0.5" y1="0" x2="6.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-0.5" x2="0" y2="6.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="6.3,0 6.1,0.08 6.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,6.3 0.08,6.1 -0.08,6.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="3" y1="0.05" x2="3" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="4" y1="0.05" x2="4" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="5" y1="0.05" x2="5" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="4" x2="-0.05" y2="4" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="5" x2="-0.05" y2="5" stroke="black" stroke-width="0.05"/><!-- Парабола y = (x - 3)^2 --><path d="M 0.5 6.25 L 1 4 L 2 1 L 3 0 L 4 1 L 5 4 L 5.5 6.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="3" cy="0" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="3.15" y="0.4" font-size="0.6">3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="6.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="6.1" font-size="0.6">y</text></svg><br><strong>г)</strong><svg width="200" height="200" viewBox="-6.5 -0.5 6.5 6.5"><!-- Оси --><line x1="-6.5" y1="0" x2="0.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-0.5" x2="0" y2="6.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="0.3,0 0.1,0.08 0.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,6.3 0.08,6.1 -0.08,6.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-5" y1="0.05" x2="-5" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-4" y1="0.05" x2="-4" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-3" y1="0.05" x2="-3" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="4" x2="-0.05" y2="4" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="5" x2="-0.05" y2="5" stroke="black" stroke-width="0.05"/><!-- Парабола y = (x + 3)^2 --><path d="M -5.5 6.25 L -5 4 L -4 1 L -3 0 L -2 1 L -1 4 L -0.5 6.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="-3" cy="0" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="-2.85" y="0.4" font-size="0.6">-3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="0.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="6.1" font-size="0.6">y</text></svg>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "2801" "height" => 1239 "path" => "/media/algebra_10/Abylkasymova-u/0-prceb28/12-1.webp?ts=1753263213" ] ] ] #original: array:7 [ "id" => 1291014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1113679" "type" => "task" ] "text" => "<p><strong>12.</strong> На каком рисунке изображен график функции $y = (x - 3)^2$:</p><p><strong>A)</strong> а; B) б; C) в; D) г?</p><br><strong>а)</strong><svg width="200" height="200" viewBox="-3.5 -3.5 7 7"><!-- Оси --><line x1="-3.5" y1="0" x2="3.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-3.5" x2="0" y2="3.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="3.3,0 3.1,0.08 3.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,3.3 0.08,3.1 -0.08,3.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-2" x2="-0.05" y2="-2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-1" x2="-0.05" y2="-1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><!-- Парабола y = -x^2 + 3 --><path d="M -2.5 -3.25 L -2 -1 L -1 2 L 0 3 L 1 2 L 2 -1 L 2.5 -3.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="0" cy="3" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="0.15" y="3.2" font-size="0.6">3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="3.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="3.1" font-size="0.6">y</text></svg><br><strong>б)</strong><svg width="200" height="200" viewBox="-3.5 -3.5 7 7"><!-- Оси --><line x1="-3.5" y1="0" x2="3.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-3.5" x2="0" y2="3.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="3.3,0 3.1,0.08 3.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,3.3 0.08,3.1 -0.08,3.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-2" x2="-0.05" y2="-2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="-1" x2="-0.05" y2="-1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><!-- Парабола y = x^2 - 3 --><path d="M -2.5 3.25 L -2 1 L -1 -2 L 0 -3 L 1 -2 L 2 1 L 2.5 3.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="0" cy="-3" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="0.15" y="-2.8" font-size="0.6">-3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="3.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="3.1" font-size="0.6">y</text></svg><br><strong>в)</strong><svg width="200" height="200" viewBox="-0.5 -0.5 6.5 6.5"><!-- Оси --><line x1="-0.5" y1="0" x2="6.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-0.5" x2="0" y2="6.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="6.3,0 6.1,0.08 6.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,6.3 0.08,6.1 -0.08,6.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="1" y1="0.05" x2="1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="2" y1="0.05" x2="2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="3" y1="0.05" x2="3" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="4" y1="0.05" x2="4" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="5" y1="0.05" x2="5" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="4" x2="-0.05" y2="4" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="5" x2="-0.05" y2="5" stroke="black" stroke-width="0.05"/><!-- Парабола y = (x - 3)^2 --><path d="M 0.5 6.25 L 1 4 L 2 1 L 3 0 L 4 1 L 5 4 L 5.5 6.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="3" cy="0" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" fill="black"/><!-- Подписи --><text x="3.15" y="0.4" font-size="0.6">3</text><text x="0.15" y="0.4" font-size="0.6">O</text><text x="6.2" y="0.4" font-size="0.6">x</text><text x="0.25" y="6.1" font-size="0.6">y</text></svg><br><strong>г)</strong><svg width="200" height="200" viewBox="-6.5 -0.5 6.5 6.5"><!-- Оси --><line x1="-6.5" y1="0" x2="0.3" y2="0" stroke="black" stroke-width="0.05"/><line x1="0" y1="-0.5" x2="0" y2="6.3" stroke="black" stroke-width="0.05"/><!-- Стрелки на осях --><polyline points="0.3,0 0.1,0.08 0.1,-0.08" stroke="black" stroke-width="0.05" fill="black"/><polyline points="0,6.3 0.08,6.1 -0.08,6.1" stroke="black" stroke-width="0.05" fill="black"/><!-- Деления на осях --><line x1="-5" y1="0.05" x2="-5" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-4" y1="0.05" x2="-4" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-3" y1="0.05" x2="-3" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-2" y1="0.05" x2="-2" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="-1" y1="0.05" x2="-1" y2="-0.05" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="1" x2="-0.05" y2="1" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="2" x2="-0.05" y2="2" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="3" x2="-0.05" y2="3" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="4" x2="-0.05" y2="4" stroke="black" stroke-width="0.05"/><line x1="0.05" y1="5" x2="-0.05" y2="5" stroke="black" stroke-width="0.05"/><!-- Парабола y = (x + 3)^2 --><path d="M -5.5 6.25 L -5 4 L -4 1 L -3 0 L -2 1 L -1 4 L -0.5 6.25" fill="none" stroke="black" stroke-width="0.1"/><!-- Точки --><circle cx="-3" cy="0" r="0.1" fill="black"/><circle cx="0" cy="0" r="0.1" 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Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1112} 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"task" ] "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "900" "height" => 192 "path" => "/media/algebra_10/Abylkasymova-u/1-prceb28/12-1.webp?ts=1753263457" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1549720 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1117 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1120} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1121} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1122} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1113679" "type" => "task" ] "text" => "<p>Для того чтобы определить, какой из графиков соответствует функции $y = (x - 3)^2$, проанализируем эту функцию.</p><p><strong>1.</strong> Это квадратичная функция, её график — парабола.</p><p><strong>2.</strong> График функции $y = (x - 3)^2$ можно получить из графика стандартной параболы $y = x^2$ путем сдвига.</p><p><strong>3.</strong> Общее правило преобразования графиков гласит, что график функции $y = f(x - a)$ получается сдвигом графика $y = f(x)$ на $a$ единиц вдоль оси Ox. Если $a > 0$, сдвиг происходит вправо, если $a < 0$ — влево.</p><p><strong>4.</strong> В нашем случае $f(x) = x^2$ и $a = 3$. Так как $a = 3 > 0$, мы должны сдвинуть график параболы $y = x^2$ на 3 единицы вправо.</p><p><strong>5.</strong> Вершина параболы $y = x^2$ находится в точке $(0, 0)$. После сдвига на 3 единицы вправо, вершина новой параболы $y = (x - 3)^2$ будет находиться в точке $(0+3, 0)$, то есть в точке $(3, 0)$.</p><p><strong>6.</strong> Коэффициент перед скобкой в квадрате равен 1 (положительное число), значит, ветви параболы направлены вверх.</p><p>Теперь рассмотрим предложенные рисунки:</p><p><strong>а)</strong> На этом графике изображена парабола, ветви которой направлены вниз, а вершина находится в точке $(0, 3)$. Это неверно.</p><p><strong>б)</strong> На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(0, -3)$. Это неверно.</p><p><strong>в)</strong> На этом графике изображена парабола с ветвями вверх и вершиной в точке $(3, 0)$. Это полностью соответствует нашему анализу.</p><p><strong>г)</strong> На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(-3, 0)$. Этот график соответствует функции $y = (x + 3)^2$. Это неверно.</p><p>Таким образом, правильный график изображен на рисунке <strong>в</strong>.</p><p><strong>Ответ:</strong> C) в.</p>" ] #original: array:6 [ "id" => 1549720 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "task" => array:2 [ "refs" => "1113679" "type" => "task" ] "text" => "<p>Для того чтобы определить, какой из графиков соответствует функции $y = (x - 3)^2$, проанализируем эту функцию.</p><p><strong>1.</strong> Это квадратичная функция, её график — парабола.</p><p><strong>2.</strong> График функции $y = (x - 3)^2$ можно получить из графика стандартной параболы $y = x^2$ путем сдвига.</p><p><strong>3.</strong> Общее правило преобразования графиков гласит, что график функции $y = f(x - a)$ получается сдвигом графика $y = f(x)$ на $a$ единиц вдоль оси Ox. Если $a > 0$, сдвиг происходит вправо, если $a < 0$ — влево.</p><p><strong>4.</strong> В нашем случае $f(x) = x^2$ и $a = 3$. Так как $a = 3 > 0$, мы должны сдвинуть график параболы $y = x^2$ на 3 единицы вправо.</p><p><strong>5.</strong> Вершина параболы $y = x^2$ находится в точке $(0, 0)$. После сдвига на 3 единицы вправо, вершина новой параболы $y = (x - 3)^2$ будет находиться в точке $(0+3, 0)$, то есть в точке $(3, 0)$.</p><p><strong>6.</strong> Коэффициент перед скобкой в квадрате равен 1 (положительное число), значит, ветви параболы направлены вверх.</p><p>Теперь рассмотрим предложенные рисунки:</p><p><strong>а)</strong> На этом графике изображена парабола, ветви которой направлены вниз, а вершина находится в точке $(0, 3)$. Это неверно.</p><p><strong>б)</strong> На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(0, -3)$. Это неверно.</p><p><strong>в)</strong> На этом графике изображена парабола с ветвями вверх и вершиной в точке $(3, 0)$. Это полностью соответствует нашему анализу.</p><p><strong>г)</strong> На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(-3, 0)$. Этот график соответствует функции $y = (x + 3)^2$. Это неверно.</p><p>Таким образом, правильный график изображен на рисунке <strong>в</strong>.</p><p><strong>Ответ:</strong> C) в.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1113680" "type" => "task" ] "previous" => array:2 [ "refs" => "1113678" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1343 #items: array:1 [ 0 => App\Models\BookPage {#1128 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true 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№12 (с. 30)
Условие. №12 (с. 30)
скриншот условия
12. На каком рисунке изображен график функции $y = (x - 3)^2$:
A) а; B) б; C) в; D) г?
а)
б)
в)
г)
Решение. №12 (с. 30)
Решение 2. №12 (с. 30)
Для того чтобы определить, какой из графиков соответствует функции $y = (x - 3)^2$, проанализируем эту функцию.
1. Это квадратичная функция, её график — парабола.
2. График функции $y = (x - 3)^2$ можно получить из графика стандартной параболы $y = x^2$ путем сдвига.
3. Общее правило преобразования графиков гласит, что график функции $y = f(x - a)$ получается сдвигом графика $y = f(x)$ на $a$ единиц вдоль оси Ox. Если $a > 0$, сдвиг происходит вправо, если $a < 0$ — влево.
4. В нашем случае $f(x) = x^2$ и $a = 3$. Так как $a = 3 > 0$, мы должны сдвинуть график параболы $y = x^2$ на 3 единицы вправо.
5. Вершина параболы $y = x^2$ находится в точке $(0, 0)$. После сдвига на 3 единицы вправо, вершина новой параболы $y = (x - 3)^2$ будет находиться в точке $(0+3, 0)$, то есть в точке $(3, 0)$.
6. Коэффициент перед скобкой в квадрате равен 1 (положительное число), значит, ветви параболы направлены вверх.
Теперь рассмотрим предложенные рисунки:
а) На этом графике изображена парабола, ветви которой направлены вниз, а вершина находится в точке $(0, 3)$. Это неверно.
б) На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(0, -3)$. Это неверно.
в) На этом графике изображена парабола с ветвями вверх и вершиной в точке $(3, 0)$. Это полностью соответствует нашему анализу.
г) На этом графике изображена парабола с ветвями вверх, но ее вершина находится в точке $(-3, 0)$. Этот график соответствует функции $y = (x + 3)^2$. Это неверно.
Таким образом, правильный график изображен на рисунке в.
Ответ: C) в.
Другие задания:
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