91Ó°ÊÓ

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where,$a≠0$ is called the standard form of the quadratic function.

The graph of the function$y=a{x}^2+bx+c$

Opens upward and has a minimum value at $x=−\frac{b}{2a}$, when $a>0$.

Opens downward and has a maximum value at $x=−\frac{b}{2a}$, when $a<0$.

The $y$-intercept of the function$y=a{x}^2+bx+c$ is always at$c$.

Compare the quadratic function $y=−2x^2−8x+2$with the standard quadratic function $y=a{x}^2+bx+c$.

$a=−2,\text{ }b=−8,\text{ }c=2$

Substitute$a=−2$and$b=−8$in $x=−\frac{b}{2a}$.

$$\begin{gathered} x=−\left(\frac{−8}{2\left(−2\right)}\right) \\ x=−\left(\frac{−8}{−4}\right) \\ x=−\left(2\right) \\ x=−2 \end{gathered}$$

Since, $a<0$.

So, the graph opens downward and has a maximum value at $x=−2$.

Since, the $y$-intercept is given by $c$.

So, the $y$-intercept is 2.

The graph of the function $y=−2x^2−8x+2$is shown below.