Question

Graph $x=-2(y+3{)}^2+2$using properties.

Short answer

The graph is

Step-by-step solution

Given information

Given function$x=-2(y+3{)}^2+2$

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

Comparing, we get

$$\begin{gathered} x=-2(y+3{)}^2+2 \\ a=-2 \\ (h,k)=(2,-3) \end{gathered}$$

As $a=-2$, parabola opens to the left

The axis of symmetry is$y=-3$

Calculate the x intercept

Calculating, we get

$$\begin{gathered} x=-2(y+3{)}^2+2 \\ x=-2{(0+3)}^2+2 \\ x=-16 \end{gathered}$$

Calculate y intercept 

Calculating, we get

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

Sketching the graph

The graph is