Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises: 55

Answer

The intercepts with $y$ axis are $-\sqrt{2}$ and $\sqrt{2}$. The intercept with $x$ axis is $6$. The graph is symmetric with respect to $x$ axis and is shown on the figure.
1492794635

Work Step by Step

To find the intercept with $y$ axis put $x=0$ and calculate $y$: $$0+3y^2 = 6\Rightarrow 3y^2=6\Rightarrow y^2=2\Rightarrow y=\pm\sqrt{2}$$ so there are two intercepts with $y$ axis $y=-\sqrt{2}$ and $y=\sqrt{2}$. To find the intercept with $x$ axis put $y=0$ and calculate $x$: $$x+3\times0^2=6\Rightarrow x=6.$$ The graph is symmetric with respect to $x$ axis because if we put $-y$ instead of $y$ we obtain the same equation $$x+3(-y)^2 = x+3y^2 = 6.$$
Small 1492794635
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.