Chapter 9.2, Problem 8CYU

To determine

To find: The graph for each of the equation.

Answer to Problem 8CYU

The graph for the parabola is shown in Figure 1

Explanation of Solution

Given:

The given equation is $x=3y^2-6y+9$ .

Calculation:

Consider the given equation is,

  $x=3y^2-6y+9$

Consider the general vertex form is,

  $x=a\left(y-k\right)+h$

Here, $\left(h,k\right)$ are the vertex, $x$ is the axis of symmetry.

Then, the vertex form is $\left(h,k\right)=\left(6,1\right)$

The axis of symmetry is $x=-5$ .

The value of $a=3$ . As it is positive the parabola open upwards.

The expression for the focus of the parabola is

  $\begin{array}{c}\left(h+\frac{1}{4a},k\right)=\left(6+\frac{1}{12},1\right)\\ =\left(\frac{73}{12},1\right)\end{array}$

The directrix of the graph is,

  $\begin{array}{c}x=h-\frac{1}{4a}\\ =6-\frac{1}{4\left(3\right)}\\ =\frac{71}{12}\end{array}$

Then, the graph for the parabola is shown in Figure 1

  

Figure 1