Question

In the following exercises, graph each equation by using properties.

$y=-x^2+8x-15$

Short answer

The graph is

Step-by-step solution

Given information

Given function$y=-x^2+8x-15$

State in standard form

Stating, we get

$$\begin{gathered} y=-x^2+8x-15 \\ y=-x^2+4·2·x-4^2-15+16 \\ y=-{(x-4)}^2-15+16 \\ y=-{(x-4)}^2+1 \end{gathered}$$

Identify the constants a, h, k and the other parameters

Comparing, we get

$$\begin{gathered} a=-1 \\ (h,k)=(4,1) \end{gathered}$$

The axis of symmetry is$x=4$

Calculate the y intercept

Calculating, we get

$$\begin{gathered} y=-{(x-4)}^2+1 \\ y=-{(0-4)}^2+1 \\ y=-15 \end{gathered}$$

Calculate the x intercept

Calculating, we get

$$\begin{gathered} y=-{(x-4)}^2+1 \\ -{(x-4)}^2+1=0 \\ -{(x-4)}^2=-1 \\ x-4=\pm 1 \\ x=5,3 \end{gathered}$$

Sketching the graph

The graph is