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Q 26.

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 643

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
line of directix $x = - \frac{1}{2}$ and vertex at the point $(0, 0)$ .

The equation of a parabola is $y^{2} = 2 x$ . The two points are $(\frac{1}{2}, 1)$ and $(\frac{1}{2}, - 1)$ .

The graph of an equation is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given vertex is at the point $(0, 0)$ and the line of directix is $x = - \frac{1}{2}$ .

Step 2. Equation of a Parabola.

A parabola whose focus is at $(\frac{1}{2}, 0)$ and whose directix is the line $x = - \frac{1}{2}$ has its vertex at $(0, 0)$ .The equation of a parabola is of the form as

$y^{2} = 4 a x y^{2} = 2 x$

where $a = \frac{1}{2}$ .

Step 3. Latus Rectum.

The two points that determines the latus rectum by letting $x = \frac{1}{2}$ .Then,

$y^{2} = 2 x y^{2} = 2 (\frac{1}{2}) y^{2} = 1 y = \pm 1$ .

The points are $(\frac{1}{2}, 1)$ and $(\frac{1}{2}, - 1)$ .

Step 4. Graphing Utility.

The graph of a parabola is

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$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

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