Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Finding the Equation of a Parabola
Find an equation of the parabola whose graph is shown

The equation of parabola is $y^{2} = x$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Graph of parabola is given as-

Step 2. Concept used

The equation of a parabola having a vertex at origin is –

$y^{2} = 4 p x$

Where, $p > 0$ then parabola opens to the right

$p < 0$ then parabola opens to the left.

The directrix is the right side of $y$ -axis is so, which means the focus should be negative, the parabola opens to the left and the coordinates of focus are obtained. On substituting the value of $p$ in the equation $y^{2} = 4 p x$ to obtain an equation of a parabola.

Step 3. Calculation

Substituting the point $(4, - 2)$ in the equation of parabola $y^{2} = 4 p x$ , we get –

${(- 2)}^{2} = 4 p (4)$

$\begin{array}{l} \Rightarrow 4 = 16 p \\ \Rightarrow 16 p = 4 \\ \Rightarrow p = \frac{4}{16} \\ \Rightarrow p = \frac{1}{4} \end{array}$

Now, substituting the value of $p$ in equation $y^{2} = 4 p x$ , we get the equation as.

$\begin{array}{l} y^{2} = 4 (\frac{1}{4}) x \\ \Rightarrow y^{2} = x \end{array}$

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Precalculus Mathematics for Calculus

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Short Answer

Finding the Equation of a Parabola
Find an equation of the parabola whose graph is shown

Step by Step Solution

Step 1. Given information

Step 2. Concept used

Step 3. Calculation

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Precalculus Mathematics for Calculus

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Short Answer

Finding the Equation of a ParabolaFind an equation of the parabola whose graph is shown

Step by Step Solution

Step 1. Given information

Step 2. Concept used

Step 3. Calculation

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Finding the Equation of a Parabola
Find an equation of the parabola whose graph is shown