Chapter 11.1, Problem 9E

To determine

To match: the equation with the graph.

Answer to Problem 9E

  

Explanation of Solution

Given information:

The equation is $y^2-8x=0$ .

First write the equation in a standard form of parabola,

  $y^2-8x$

Comparing the standard form of the parabola to the general equation,

  $y^2-4px$

By comparing the equations it can be observed that,

  $\begin{array}{l}4p=8\\ p=2\text{ [divide]}\end{array}$

Directrix: the directrix of parabola is given by $x=-p$ ,

Since $p=2$ , substitute it,

  $\begin{array}{l}x=-p\\ x=-2\text{ [substitute p by }2]\end{array}$

So the directrix of the parabola is $x=-2$ .

Focus: the focus of parabola is given as $F\left(p,0\right)$ ,

Since $p=2$ , substitute the value of $p$ ,

Thus, the focus of parabola is $F\left(2,0\right)$ .

Vertices : $\left(0,0\right)$

Since the $\text{p>0}$ , so the parabola is opened to the right.

Use the above information together with some additional values which is show in table below

To sketch the graph,

x	y
1	2.82
2	4
3	4.89
4	5.65

The graph is obtained as: