Задание
Выберите график квадратичной функции \(\displaystyle y=3x^2{\small :}\)
| \(\displaystyle 1\) |  | \(\displaystyle 2\) |  |
| \(\displaystyle 3\) |  | \(\displaystyle 4\) |  |
Решение
Построим график квадратичной функции \(\displaystyle y=3x^2\) по точкам. Для этого составим таблицу значений:
| \(\displaystyle x\) | \(\displaystyle 0\) | \(\displaystyle 0{,}2\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) | \(\displaystyle 1{,}2\) |
| \(\displaystyle y=3x^2\) | \(\displaystyle 0\) | \(\displaystyle 0{,}12\) | \(\displaystyle 0{,}48\) | \(\displaystyle 1{,}08\) | \(\displaystyle 1{,}92\) | \(\displaystyle 3\) | \(\displaystyle 4{,}32\) |
и симметрично отрицательные значения по оси ОХ:
| \(\displaystyle x\) | \(\displaystyle -1{,}2\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}2\) | \(\displaystyle 0\) |
| \(\displaystyle y=3x^2\) | \(\displaystyle 4{,}32\) | \(\displaystyle 3\) | \(\displaystyle 1{,}92\) | \(\displaystyle 1{,}08\) | \(\displaystyle 0{,}48\) | \(\displaystyle 0{,}12\) | \(\displaystyle 0\) |
Обозначим данные точки на плоскости:
и соединим их:
Сравнивая графики
| \(\displaystyle 1\) | | \(\displaystyle 2\) | |
| \(\displaystyle 3\) | | \(\displaystyle 4\) | |
получаем, что графику квадратичной функции \(\displaystyle y=3x^2\) соответствует вариант \(\displaystyle 4{\small .}\)
Ответ: \(\displaystyle 4{\small .}\)