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

Задание

Дана квадратичная функция \(\displaystyle y=x^2{\small .}\) Вычислите значения функции в заданных точках:
 

\(\displaystyle x\)\(\displaystyle -2\)\(\displaystyle -1{,}7\)\(\displaystyle -1{,}5\)\(\displaystyle -1\)\(\displaystyle -0{,}5\)\(\displaystyle 0\)\(\displaystyle 0{,}5\)\(\displaystyle 1\)\(\displaystyle 1{,}5\)\(\displaystyle 1{,}7\)\(\displaystyle 2\)
\(\displaystyle y=x^2\)


Выберите график с точками, лежащими на графике квадратичной функции \(\displaystyle y=x^2{\small :}\)

\(\displaystyle \rm I\)\(\displaystyle \rm II\)
\(\displaystyle \rm III\)\(\displaystyle \rm IV\)
 
Решение

Вычислим значение квадратичной функции \(\displaystyle y=x^2\) в заданных точках:
 

\(\displaystyle x\)\(\displaystyle -2\)\(\displaystyle -1{,}7\)\(\displaystyle -1{,}5\)\(\displaystyle -1\)\(\displaystyle -0{,}5\)\(\displaystyle 0\)\(\displaystyle 0{,}5\)\(\displaystyle 1\)\(\displaystyle 1{,}5\)\(\displaystyle 1{,}7\)\(\displaystyle 2\)
\(\displaystyle y=x^2\)\(\displaystyle 4\)\(\displaystyle 2{,}89\)\(\displaystyle 2{,}25\)\(\displaystyle 1\)\(\displaystyle 0{,}25\)\(\displaystyle 0\)\(\displaystyle 0{,}25\)\(\displaystyle 1\)\(\displaystyle 2{,}25\)\(\displaystyle 2{,}89\)\(\displaystyle 4\)


Отметим  точки

\(\displaystyle (-2;\, 4),\, (-1{,}7;\, 2{,}89),\, (-1{,}5;\, 2{,}25),\, (-1;\, 1),\, (-0{,}5;\, 0{,}25),\, (0;\, 0),\)

\(\displaystyle (0{,}5;\, 0{,}25),\, (1;\, 1),\, (1{,}5;\, 2{,}25),\, (1{,}7;\, 2{,}89),\,(2;\, 4)\)

на координатной плоскости:
 


Сравним с данными графиками:
 

\(\displaystyle \rm I\)\(\displaystyle \rm II\)
\(\displaystyle \rm III\)\(\displaystyle \rm IV\)

 

Видим, что график \(\displaystyle \rm II\) соответствует нашей квадратичной функции \(\displaystyle y=x^2{\small .}\)

Ответ:  \(\displaystyle \rm II {\small .}\)