Question

Graph $x=3(y-1{)}^2+2$using properties.

Short answer

The graph is

Step-by-step solution

Given information

Given the function$x=3(y-1{)}^2+2$

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

Comparing, we get

$$\begin{gathered} x=3(y-1{)}^2+2 \\ a=3 \\ (h,k)=(2,1) \end{gathered}$$

As $a=3$, parabola opens to the right

Calculate the x intercepts

Substituting $y=0$, we get

role="math" localid="1645190065504" $$\begin{gathered} x=3(y-1{)}^2+2 \\ x=3{(0-1)}^2+2 \\ x=5 \end{gathered}$$

Calculate y intercept

Calculating, we get

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

Square can't be negative so there will no $y$intercepts

A symmetrical point is$(5,2)$

Sketching of graph

The graph is