Question

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

$y=-x^2+4x-3$

Short answer

The graph is

Step-by-step solution

Given information

Given the function$y=-x^2+4x-3$

State in standard form

Comparing, we get

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

Comparing, we get

$$\begin{gathered} y={(x-2)}^2+1 \\ a=1 \\ (h,k)=(2,1) \end{gathered}$$

As $a=1$, the parabola opens to the right

Calculate the y intercept

Calculating, we get

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

Calculate the x intercept

Calculating, we get

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

The axis of symmetry is$x=2$

Sketching the graph

The graph is