Chapter 11: Q.72 (page 1101)

In the following exercises, graph each equation by using properties.
$x = - {(y - 4)}^{2} + 3$

Short Answer

Expert verified

The graph of the equation is

Step by step solution

Step 1. Given Information

Given equation of the parabola is $x = - {(y - 4)}^{2} + 3$

The graph of the parabola is to be determined

Step 2. Equation of the parabola

The equation of a parabola in standard form $x = a {(y - k)}^{2} + h$

The given equation is $x = - {(y - 4)}^{2} + 3$

Here $a = - 1, k = 4, h = 3$

Since a is negative, the parabola opens to the left.

Step 3. Axis of symmetry

The axis of symmetry of the parabola $x = a {(y - k)}^{2} + h$ is $y = k$

Plugging the values:

$y = 4$

Hence the axis of symmetry is $y = 4$

Step 4. Vertex of a parabola

The vertex of the parabola $x = a {(y - k)}^{2} + h$ is $(h, k)$

The vertex of the given parabola is $(3, 4)$

Step 5. Intercepts

x-intercept is the point where the graph crosses the x-axis and y is 0.

y-intercept is the point where the graph crosses the y-axis and x is 0.

x-intercept:

Plugging $y = 0$ in the equation:

$x = - {(y - 4)}^{2} + 3 x = - {(0 - 4)}^{2} + 3 x = - {(- 4)}^{2} + 3 x = - 16 + 3 x = - 13$

Hence the x-intercept is $(- 13, 0)$

y-intercept:

Plugging $x = 0$ in the equation:

localid="1645420661627" $x = - {(y - 4)}^{2} + 3 0 = - {(y - 4)}^{2} + 3 {(y - 4)}^{2} = 3 y - 4 = \pm \sqrt{3} y = \pm \sqrt{3} + 4$

Hence y-intercepts are $(0, \sqrt{3} + 4), (0, - \sqrt{3} + 4)$

Step 6. Plotting points

Since, the vertex and intercepts are only two points, more points are needed to plot the parabola.

Hence assuming few y values and finding the corresponding x values to points can be obtained.

When $y = 1$ :

$x = - {(y - 4)}^{2} + 3 x = - {(1 - 4)}^{2} + 3 x = - {(- 3)}^{2} + 3 x = - 9 + 3 x = - 6$

When $y = - 1$ :

$x = - {(y - 4)}^{2} + 3 x = - {(- 1 - 4)}^{2} + 3 x = - {(- 5)}^{2} + 3 x = - 25 + 3 x = - 22$

Hence the points are role="math" localid="1645420960151" $(- 6, 1), (- 22, - 1)$

Step 7. Graphing the parabola

Using the properties, plotting the points and graphing the parabola:

Conclusion

The graph of the parabola is

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 exercises, graph each equation by using properties.
$x = - {(y - 4)}^{2} + 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the parabola

Step 3. Axis of symmetry

Step 4. Vertex of a parabola

Step 5. Intercepts

Step 6. Plotting points

Step 7. Graphing the parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.x=-(y-4)2+3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the parabola

Step 3. Axis of symmetry

Step 4. Vertex of a parabola

Step 5. Intercepts

Step 6. Plotting points

Step 7. Graphing the parabola

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.
$x = - {(y - 4)}^{2} + 3$