   # Further Investigations The points ( x , y ) and ( y , x ) are mirror images of each other across the line y = x . Therefore, by interchanging x and y in the equation y = a x 2 + b x + c , we obtain the equation of its mirror image across the line y = x ; namely, x = a y 2 + b y + c . Thus to graph x = y 2 + 2 , we can first graph y = x 2 + 2 and then reflect it across the line y = x , as indicated in Figure 8.22. Graph each of the following parabolas. x = y 2 x = − y 2 x = y 2 − 1 x = − y 2 + 3 x = − 2 y 2 x = 3 y 2 x = y 2 + 4 y + 7 x = y 2 − 2 y − 3 Figure 8.22 ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 8.2, Problem 62PS
Textbook Problem
1 views

## Further InvestigationsThe points ( x , y ) and ( y , x ) are mirror images of each other across the line y = x . Therefore, by interchanging x and y in the equation y = a x 2 + b x + c , we obtain the equation of its mirror image across the line y = x ; namely, x = a y 2 + b y + c . Thus to graph x = y 2 + 2 , we can first graph y = x 2 + 2 and then reflect it across the line y = x , as indicated in Figure 8.22.Graph each of the following parabolas. x = y 2 x = − y 2 x = y 2 − 1 x = − y 2 + 3 x = − 2 y 2 x = 3 y 2 x = y 2 + 4 y + 7 x = y 2 − 2 y − 3 Figure 8.22

To determine

(a)

To graph:

The given parabola x=y2.

### Explanation of Solution

Given:

The points (x,y) and (y,x) are mirror images of each other across the line y=x. Therefore, by interchanging x and y in the equation y=ax2+bx+c, obtain the equation of its mirror image across the line y=x; namely, x=ay2+by+c. Thus to graph x=y2+2, first graph y=x2+2 and then reflect it across the line y=x, as indicated in Figure (1)

To determine

(b)

To graph:

The given parabola x=y2.

To determine

(c)

To graph:

The given parabola x=y21.

To determine

(d)

To graph:

The given parabola x=y2+3.

To determine

(e)

To graph:

The given parabola x=2y2.

To determine

(f)

To graph:

The given parabola x=3y2.

To determine

(g)

To graph:

The given parabola x=y2+4y+7.

To determine

(h)

To graph:

The given parabola x=y22y3.

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