Chapter 9.2, Problem 9CYU

To determine

To find: The equation for the parabola from the given data and graph the equation.

Answer to Problem 9CYU

The equation for the parabola is $y=\frac{1}{8}{x}^2+2$ and the graph for the parabola is shown in Figure 1

Explanation of Solution

Given:

The vertex of the equation is $\left(0,2\right)$ and focus for the $\left(0,4\right)$ .

Calculation:

Consider the general vertex form is,

  $y=a{\left(x-h\right)}^2+k$

Here, $\left(h,k\right)$ is the vertex and focus of the parabola is $\left(h,k+\frac{1}{4a}\right)$ .

Then, the focus is calculated as,

  $\begin{array}{l}k+\frac{1}{4a}=4\\ 2+\frac{1}{4a}=4\\ a=\frac{1}{8}\end{array}$

Thus, the equation of the parabola is,

  $y=\frac{1}{8}{x}^2+2$

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

  

Figure 1