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Chapter 11: Q. 70 (page 715)

Find real numbers a, b, and c so that the

graph of the function y=ax2+bx+ccontains 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

01

Given information

We are given a equationy=ax2+bx+c

02

Find the equations

The equation satisfies the points Therefore

for(x,y)=(-1,-2)-2=a-b+c(1)for(x,y)=(1,-4)-4=a+b+c(2)for(x,y)=(2,4)4=4a+2b+c(3)

03

Solve the equation 

To solve the equation

Add equation 1 and 2

a-b+c=-2+a+b+c=-42a+2c=-6

hence we have

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

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

2a-2b+2c=-4+4a+2b+c=46a+3c=0

Hence 6a+3c=02a+c=0(5)

Subtract equation 4 and 5 we get

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

Therefore a=3

Find the values of b ,c

a+c=-33+c=-3c=-6

Similarly

a-b+c=-23-b-6=-2b=-1

04

Conclusion

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

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