Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 9 Quadratic Relations and Conic Sections - 9.2 Graph and Write Equations of Parabolas - Guided Practice for Examples 1 and 2 - Page 622: 1

Answer

Focus: $\left(-\frac{3}{2},0\right)$ Directrix: $x=\frac{3}{2}$ Axis of symmetry: $x$-axis

Work Step by Step

$\bf{Step\text{ }1}$ The equation is in standard form: $$y^2=-6x.$$ $\bf{Step\text{ }2}$ We identify the focus, directrix and axis of symmetry. The equation has the form $y^2=4px$, where $p=-\frac{3}{2}$. The $\bf{focus}$ is $(p,0)$ or $\left(-\frac{3}{2},0\right)$. The $\bf{directrix}$ is $x=-p$ or $x=\frac{3}{2}$. Because $y$ is squared, the $\bf{axis\text{ } of\text{ }symmetry}$ is the $x$-axis. $\bf{Step\text{ }3}$ We $\bf{draw}$ the parabola by making a table of values and plotting points. As $p<0$, the parabola opens to the left. So we will use only negative $x$-values. \[ \begin{array}{cccccc} x &|& -1 &|& -2 &|& -3 &|& -4 &|& -5 &|&\\ y &|& \pm 2.49 &|& \pm 3.46 &|& \pm 4.24 &|& \pm 4.90 &|& \pm5.48 &|&\\ \end{array}\]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.