Question

Graph the function.

$y=-2x^2-8x+2$

Short answer

The graph of the function$y=-2x^2-8x+2$ 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=−2x2−8x+2.

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

$a=-2,b=-8,c=2$

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.