Задание
Заполните таблицу значений квадратичной функции \(\displaystyle y=x^2{\small :}\)
| \(\displaystyle x\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}3\) | \(\displaystyle 0\) | \(\displaystyle 0{,}3\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) |
| \(\displaystyle y=x^2\) |
Мысленно постройте график квадратичной функции \(\displaystyle y=x^2\) по полученным точкам:
Решение
Заполним таблицу значений квадратичной функции \(\displaystyle y=x^2{\small :}\)
| \(\displaystyle x\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}3\) | \(\displaystyle 0\) | \(\displaystyle 0{,}3\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) |
| \(\displaystyle y=x^2\) | \(\displaystyle (-1)^2\) | \(\displaystyle (-0{,}8)^2\) | \(\displaystyle (-0{,}6)^2\) | \(\displaystyle (-0{,}4)^2\) | \(\displaystyle (-0{,}3)^2\) | \(\displaystyle 0\) | \(\displaystyle 0{,}3^2\) | \(\displaystyle 0{,}4^2\) | \(\displaystyle 0{,}6^2\) | \(\displaystyle 0{,}8^2\) | \(\displaystyle 1^2\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}3\) | \(\displaystyle 0\) | \(\displaystyle 0{,}3\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) |
| \(\displaystyle y=x^2\) | \(\displaystyle 1\) | \(\displaystyle 0{,}64\) | \(\displaystyle 0{,}36\) | \(\displaystyle 0{,}16\) | \(\displaystyle 0{,}09\) | \(\displaystyle 0\) | \(\displaystyle 0{,}09\) | \(\displaystyle 0{,}16\) | \(\displaystyle 0{,}36\) | \(\displaystyle 0{,}64\) | \(\displaystyle 1\) |
Построим точки на плоскости:
Соединим полученные точки:
Получили график функции \(\displaystyle y=x^2\) на отрезке \(\displaystyle [-1{\small ;}1]{\small .} \)
Замечание / комментарий
Построение по точкам
Чем больше возьмём точек с абсциссами от \(\displaystyle -1 \) до \(\displaystyle 1{\small , } \) тем точнее сможем изобразить график функции \(\displaystyle y=x^2\) на отрезке \(\displaystyle [-1{\small ;}1]{\small : } \)
