Chapter 11: Q.88 (page 1102)

In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

Short Answer

Expert verified

The equation of the given graph is $e) y = - x^{2} + 8 x - 15$

Step by step solution

Step 1. Given Information

Given graph is

Given equations to match are:

$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

The equation of the given graph among the given equations is to be determined.

Step 2. Equation of the graph

Given graph is a downward opening parabola.

The standard form of a downward opening parabola is $y = a x^{2} + b x + c$ where a is negative.

Among the given options, the only equation where a is negative is $y = - x^{2} + 8 x - 15$

Step 3. Conclusion

The equation of the given graph is $e) y = - x^{2} + 8 x - 15$

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In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the graph

Step 3. Conclusion

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In the following exercises, match each graph to one of the following equations:a)x2+y2=64b)x2+y2=49c)x+52+y+22=4d)x-22+y-32=9e)y=-x2+8x-15f)y=6x2+2x-1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the graph

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$