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Expert-verified Found in: Page 644 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.${y}^{2}=8x$

The vertex is $\left(0,0\right)$ focus is $\left(2,0\right)$ and directrix is $x=-2$ . The graph of the given equation is shown below . See the step by step solution

## Step 1. Given information .

Consider the given equation ${y}^{2}=8x$ .

## Step 2. Analyze the equation .

The standard form of parabola is ${y}^{2}=4ax$ .

Compare the equation with standard form.

${y}^{2}=4ax\phantom{\rule{0ex}{0ex}}{y}^{2}=8x\phantom{\rule{0ex}{0ex}}4a=8\phantom{\rule{0ex}{0ex}}a=2$

Further simplify .

Since $a=2$ the vertex is $\left(0,0\right)$ ,the focus is $\left(a,0\right)=\left(2,0\right)$ and the directrix is $x=-a,x=-2$

## Step[ 3. Plot the graph .

The graph of the equation ${y}^{2}=8x$ using graphing utility is shown below . Here V is the vertex , F is the focus and line $x=-2$ represents the directrix of the parabola . ### Want to see more solutions like these? 