Question

Graph the function.

$y=x^2+6x-6$

Short answer

The graph of the function$y=x^2+6x-6$ is

Step-by-step solution

Step 1. Define the standard form of the quadratic function.

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

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

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 $a<0$.

Step 3. Define y-intercept of the function y=ax2+bx+c.

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

Step 4. Plot the graph of the function y=x2+6x−6.

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

$a=1,b=6,c=-6$

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.