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Теория: Построение графика квадратичной функции \(\displaystyle \small y=kx^{2}, \,k<0\)

Задание

Построение графика квадратичной функция \(\displaystyle y=-x^2{\small :}\) на отрезке \(\displaystyle [-1;\, 1] {\small .}\)
 

\(\displaystyle x\) \(\displaystyle -1\) \(\displaystyle -0{,}8\) \(\displaystyle -0{,}6\) \(\displaystyle -0{,}4\) \(\displaystyle -0{,}3\) \(\displaystyle 0\) \(\displaystyle 0{,}3\) \(\displaystyle 0{,}4\) \(\displaystyle 0{,}6\) \(\displaystyle 0{,}8\) \(\displaystyle 1\)
\(\displaystyle y=x^2\)
Решение

Заполним таблицу значений квадратичной функции \(\displaystyle y=-x^2{\small :}\)

\(\displaystyle x\) \(\displaystyle -1\) \(\displaystyle -0{,}8\) \(\displaystyle -0{,}6\) \(\displaystyle -0{,}4\) \(\displaystyle -0{,}3\) \(\displaystyle 0\)
\(\displaystyle y=x^2\) \(\displaystyle -(-1)^2\) \(\displaystyle -(-0{,}8)^2\) \(\displaystyle -(-0{,}6)^2\) \(\displaystyle -(-0{,}4)^2\) \(\displaystyle -(-0{,}3)^2\) \(\displaystyle 0\)

 

\(\displaystyle x\) \(\displaystyle 0{,}3\) \(\displaystyle 0{,}4\) \(\displaystyle 0{,}6\) \(\displaystyle 0{,}8\) \(\displaystyle 1\)
\(\displaystyle y=x^2\) \(\displaystyle -0{,}3^2\) \(\displaystyle -0{,}4^2\) \(\displaystyle -0{,}6^2\) \(\displaystyle -0{,}8^2\) \(\displaystyle -1^2\)


Вычисляем 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:


Построим график квадратичной функции \(\displaystyle y=-x^2\) по полученным точкам, добавляя еще точки, если это необходимо:
 


Замечание / комментарий

Построение по точкам

Если построить по оси ОХ много точек с координатами от \(\displaystyle -1 \) до \(\displaystyle 1{\small , } \) то получаем следующую картинку графика: