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Chapter 11: Q. 69 (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)(2,4)

Short Answer

Expert verified

The values are

a=-43b=-53c=1

Step by step solution

01

Given information

We are given a equationy=ax2+bx+c

02

Write equations in terms of a, b,c

The equation satisfies the given points

Hence,

y=ax2+bx+cfor(x,y)=(-1,4)4=a-b+c(1)For(x,y)=(2,3)3=4a+2x+c(2)For(x,y)=(0,1)1=c(3)

03

Solve the equations

We get,

From equation 3 we have c=1

Substitute the values in equation 1 and 2 and simplify the equations

a-b+1=4a-b=3(4)Similarly4a+2b+1=34a+2b=2(5)

Now multiply equation 4 by 2 and add equation 5 to it

2a-2b=64a+2b=26a=8

Therefore a=43

Now we find b

Asa-b=3b=-3+ab=-3+43b=-53

04

Conclusion

The values of a, ,b, c are43,-53,1respectively.

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