Chapter 9.2, Problem 5CYU

To determine

To find: The graph for each of the equation.

Answer to Problem 5CYU

The graph for the parabola is shown in Figure 1

Explanation of Solution

Given:

The given equation is $y={\left(x-4\right)}^2-6$ .

Calculation:

Consider the given equation is,

  $y={\left(x-4\right)}^2-6$

Consider the general vertex form is,

  $y=a{\left(x-h\right)}^2+k$

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

Then, the vertex form is $\left(h,k\right)=\left(4,-6\right)$

The axis of symmetry is $x=4$ .

The value of $a=1$ . As it is positive the parabola open upwards.

The expression for the focus of the parabola is

  $\begin{array}{c}\left(h,k+\frac{1}{4a}\right)=\left(4,-6+\frac{1}{4}\right)\\ =\left(4,-5.75\right)\end{array}$

The directrix of the graph is,

  $\begin{array}{c}y=k-\frac{1}{4a}\\ =-6-\frac{1}{4\left(1\right)}\\ =-6.25\end{array}$

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

  

Figure 1