Question

Graph$x=-4(y+2{)}^2+4$ using properties.

Short answer

The graph is

Step-by-step solution

Given information

Given the function$x=-4(y+2{)}^2+4$

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

Comparing, we get

$$\begin{gathered} x=-4(y+2{)}^2+4 \\ a=-4 \\ (h,k)=(4,-2) \end{gathered}$$

As $a=-4$, parabola opens to the left

The axis of symmetry is$y=-2$

Calculate the x intercept

Calculating, we get

$$\begin{gathered} x=-4(y+2{)}^2+4 \\ x=-4{(0+2)}^2+4 \\ x=-12 \end{gathered}$$

Calculating the y intercept

Calculating, we get

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

Sketching the graph

The graph is