Question

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

Short answer

The graph is

Step-by-step solution

Given information

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

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 right

Calculate the x intercept

Calculating, we get

$$\begin{gathered} x=2(y-3{)}^2+2 \\ x=2{(0-3)}^2+2 \\ x=20 \end{gathered}$$

Calculate the y intercept

Calculating, we get

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

Square can't be negative so there are no $y$intercept

The symmetrical point is$(20,6)$

Sketching the graph

The graph is