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 $y=x^2+6x−6$with the standard quadratic function $y=a{x}^2+bx+c$.

$a=1,\text{ }b=6,\text{ }c=−6$

Substitute$a=1$and$b=6$in $x=−\frac{b}{2a}$.

$$\begin{gathered} x=−\left(\frac{6}{2\left(1\right)}\right) \\ x=−\left(\frac{6}{2}\right) \\ x=−\left(3\right) \\ x=−3 \end{gathered}$$

Since, $a>0$.

So, the graph opens upward and has a minimum value at $x=−3$.

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

So, the localid="1647891614457" $y$-intercept is localid="1647891621537" $−6$.

The graph of the function localid="1647891628269" $y=x^2+6x−6$is shown below.