Chapter 11: Q.273 (page 1156)

In the following exercise graph each equation by using its properties:
$x = 2 y^{2} + 4 y + 6$

Short Answer

Expert verified

The graph of the parabola can be given as

Step by step solution

Given information

We are given a equation $x = 2 y^{2} + 4 y + 6$

find whether the parabola opens Right or Left

As the coefficient of square term is positive the parabola opens to the Right

Find the axis of symmetry

To find axis of symmetry we substitute $y = - \frac{b}{2 a} y = - \frac{4}{4} y = - 1$

Find the vertex of parabola

To find the vertex put $y = - 1$ we get

$x = 2 y^{2} + 4 y + 6 x = 2 - 4 + 6 x = 4$

The vertex of parabola is $(4, - 1)$

Find the x-intercept

Put $y = 0$

we get,

$x = 2 y^{2} + 4 y + 6 x = 0 + 0 + 6 x = 6$

The coordinates are $(6, 0)$

Find the y-intercept

Put $x = 0$

$2 y^{2} + 4 y + 6 = 0 y^{2} + 2 y + 3 = 0$

On solving further we conclude that the roots of the above equation are imaginary

Hence the y-intercept is absent

Plot the graph of parabola

The graph of parabola can be given as

Conclusion

The graph of parabola can be given as

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercise graph each equation by using its properties:
$x = 2 y^{2} + 4 y + 6$

Short Answer

Step by step solution

Given information

find whether the parabola opens Right or Left

Find the axis of symmetry

Find the vertex of parabola

Find the x-intercept

Find the y-intercept

Plot the graph of parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercise graph each equation by using its properties:x=2y2+4y+6

Short Answer

Step by step solution

Given information

find whether the parabola opens Right or Left

Find the axis of symmetry

Find the vertex of parabola

Find the x-intercept

Find the y-intercept

Plot the graph of parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercise graph each equation by using its properties:
$x = 2 y^{2} + 4 y + 6$