Chapter 11: Q. 70 (page 715)

Find real numbers a, b, and c so that the
graph of the function $y = a x^{2} + b x + c$ contains the points (-1, -2), (1, -4), and (2, 4).

Short Answer

Expert verified

The values of a, ,b, c are 3, -1 ,-6

Step by step solution

Given information

We are given a equation $y = a x^{2} + b x + c$

Find the equations

The equation satisfies the points Therefore

$f o r (x, y) = (- 1, - 2) - 2 = a - b + c (1) f o r (x, y) = (1, - 4) - 4 = a + b + c (2) f o r (x, y) = (2, 4) 4 = 4 a + 2 b + c (3)$

Solve the equation

To solve the equation

Add equation 1 and 2

$a - b + c = - 2 + a + b + c = - 4 2 a + 2 c = - 6$

hence we have

$2 a + 2 c = - 6 a + c = - 3$ (4)

Now multiply the equation 1 by 2 and add it to equation 3

$2 a - 2 b + 2 c = - 4 + 4 a + 2 b + c = 4 6 a + 3 c = 0$

Hence $6 a + 3 c = 0 2 a + c = 0 (5)$

Subtract equation 4 and 5 we get

$a + c = - 3 - 2 a - c = 0 - a = - 3$

Therefore $a = 3$

Find the values of b ,c

$a + c = - 3 3 + c = - 3 c = - 6$

Similarly

$a - b + c = - 2 3 - b - 6 = - 2 b = - 1$

Conclusion

The values of a, ,b, c are 3,-1,-6 respectively

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Find real numbers a, b, and c so that the
graph of the function $y = a x^{2} + b x + c$ contains the points (-1, -2), (1, -4), and (2, 4).

Short Answer

Step by step solution

Given information

Find the equations

Solve the equation

Conclusion

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Find real numbers a, b, and c so that thegraph of the function y=ax2+bx+ccontains the points (-1, -2), (1, -4), and (2, 4).

Short Answer

Step by step solution

Given information

Find the equations

Solve the equation

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Logic and Functions

Geometry

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find real numbers a, b, and c so that the
graph of the function $y = a x^{2} + b x + c$ contains the points (-1, -2), (1, -4), and (2, 4).