Chapter 11: Q.270 (page 1156)

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = - 3 x^{2} - 18 x - 29$

Short Answer

Expert verified

The equation can be given as $y = - 3 {(x - 3)}^{2} - 2$

The graph of parabola is

Step by step solution

Step : Given information

We are given a equation of parabola $y = - 3 x^{2} - 18 x - 29$

Write the equation in standard form

We have,

$y = - 3 x^{2} - 18 x - 29 y = - 3 (x^{2} - 6 x) - 29 y = - 3 (x^{2} - 6 x + 9) + 27 - 29 y = - 3 {(x - 3)}^{2} - 2$

comparing with standard form we get

$a = - 3, h = 3, k = - 2$

Find the axis of symmetry and vertex of parabola

To find axis of symmetry put $x = h$

we get $x = 3$

The vertex of the parabola can be given as $(h, k) = (3, - 2)$

find y-intercept

To find y-intercept put $x = 0$

we get,

role="math" localid="1645501855919" $y = {(0 - 3)}^{2} - 2 y = 9 - 2 y = 7$

The coordinate can be given as $(0, 7)$

Find the point of symmetry to (0,7)across the axis of symmetry

The point of symmetry can be given as $(- 6, - 29)$

Find the x-intercept

Put $y = 0$

we get,

role="math" localid="1645502297666"

- 3 {(x - 3)}^{2} - 2 = 0 {(x - 3)}^{2} = - \frac{2}{3} x - 3 = \pm \sqrt{- \frac{2}{3}}

the roots are imaginary

Plot the graph of the parabola

the graph can be given as

Conclusion

The equation in standard form can be given as $y = - 3 {(x - 3)}^{2} - 2$

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 a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = - 3 x^{2} - 18 x - 29$

Short Answer

Step by step solution

Step : Given information

Write the equation in standard form

Find the axis of symmetry and vertex of parabola

find y-intercept

Find the point of symmetry to (0,7)across the axis of symmetry

Find the x-intercept

Plot the graph of the parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Calculus

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola: y=-3x2-18x-29

Short Answer

Step by step solution

Step : Given information

Write the equation in standard form

Find the axis of symmetry and vertex of parabola

find y-intercept

Find the point of symmetry to (0,7)across the axis of symmetry

Find the x-intercept

Plot the graph of the parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Calculus

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = - 3 x^{2} - 18 x - 29$