Chapter 11: Q.71 (page 1101)

In the following exercises, graph each equation by using properties.
$x = - {(y - 1)}^{2} + 2$

Short Answer

Expert verified

The graph of the equation is

Step by step solution

Step 1. Given Information

Given equation of the parabola is $x = - {(y - 1)}^{2} + 2$

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 $x = - {(y - 1)}^{2} + 2$

Here $a = - 1, k = 1, h = 2$

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:

$y = 1$

Hence the axis of symmetry is $y = 1$

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 $(2, 1)$

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:

localid="1645360123002" $x = - {(y - 1)}^{2} + 2 x = - {(0 - 1)}^{2} + 2 x = - {(- 1)}^{2} + 2 x = - 1 + 2 x = 1$

Hence the x-intercept is $(1, 0)$

y-intercept:

Plugging $x = 0$ in the equation:

localid="1645420321689" $x = - {(y - 1)}^{2} + 2 0 = - {(y - 1)}^{2} + 2 {(y - 1)}^{2} = 2 y - 1 = \pm \sqrt{2} y = \pm \sqrt{2} + 1$

Hence the y-intercepts are $(0, \sqrt{2} + 1), (0, - \sqrt{2} + 1)$

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 $y = 1$ :

$x = - {(y - 1)}^{2} + 2 x = - {(1 - 1)}^{2} + 2 x = - {(0)}^{2} + 2 x = - 0 + 2 x = 2$

When $y = - 1$ :

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

Hence the points are $(2, 1), (- 2, - 1)$

Step 7. Graphing the parabola

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

Conclusion

The graph of the parabola is

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In the following exercises, graph each equation by using properties.
$x = - {(y - 1)}^{2} + 2$

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

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In the following exercises, graph each equation by using properties.x=-(y-1)2+2

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

Mechanics Maths

Calculus

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using properties.
$x = - {(y - 1)}^{2} + 2$