Задание
Заполните таблицу значений квадратичной функции \(\displaystyle y=x^2{\small :}\)
| \(\displaystyle \small {x}\) | \(\displaystyle -2\) | \(\displaystyle -1,5\) | \(\displaystyle -1,2\) | \(\displaystyle -1\) | \(\displaystyle -0,5\) | \(\displaystyle 0\) | \(\displaystyle 0,5\) | \(\displaystyle 1\) | \(\displaystyle 1,2\) | \(\displaystyle 1,5\) | \(\displaystyle 2\) |
| \(\displaystyle \small { y=x^2}\) |
Мысленно постройте график квадратичной функции \(\displaystyle y=x^2\) по полученным точкам:
Решение
Заполним таблицу значений квадратичной функции \(\displaystyle y=x^2{\small :}\)
| \(\displaystyle x\) | \(\displaystyle -2\) | \(\displaystyle -1{,}5\) | \(\displaystyle -1\) | \(\displaystyle -0{,}5\) | \(\displaystyle 0\) | \(\displaystyle 0{,}5\) | \(\displaystyle 1\) | \(\displaystyle 1{,}5\) | \(\displaystyle 2\) |
| \(\displaystyle y=x^2\) | \(\displaystyle (-2)^2\) | \(\displaystyle (-1{,}5)^2\) | \(\displaystyle (-1)^2\) | \(\displaystyle (-0{,}5)^2\) | \(\displaystyle 0\) | \(\displaystyle 0{,}5^2\) | \(\displaystyle 1^2\) | \(\displaystyle 1{,}5^2\) | \(\displaystyle 2^2\) |
Вычислим значения:
| \(\displaystyle x\) | \(\displaystyle -2\) | \(\displaystyle -1{,}5\) | \(\displaystyle -1\) | \(\displaystyle -0{,}5\) | \(\displaystyle 0\) | \(\displaystyle 0{,}5\) | \(\displaystyle 1\) | \(\displaystyle 1{,}5\) | \(\displaystyle 2\) |
| \(\displaystyle y=x^2\) | \(\displaystyle 4\) | \(\displaystyle 2{,}25\) | \(\displaystyle 1\) | \(\displaystyle 0{,}25\) | \(\displaystyle 0\) | \(\displaystyle 0{,}25\) | \(\displaystyle 1\) | \(\displaystyle 2{,}25\) | \(\displaystyle 4\) |
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 \(\displaystyle [-2{\small ;}2]{\small : } \)
