Use a system of linear equations to find the quadratic function f(x) = ax^22+bx+c that satisfies the given conditions. Solve the system using matrices. f(-2) = 6, f(1) = -3, f(2) = -14 f(x) =?

a2linetagadaW 2021-01-10 Answered
Use a system of linear equations to find the quadratic function
f(x)=ax22+bx+c
that satisfies the given conditions. Solve the system using matrices.
f(-2) = 6, f(1) = -3, f(2) = -14
f(x) =?
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Expert Answer

krolaniaN
Answered 2021-01-11 Author has 86 answers
Step 1
f(x)=ax2+bx+c
f(-2)=6 , f(1)=-3 , f(2)=-14
f(-2)=6
4a2b+c=6(1)
f(1)=3
a+b+c=3(2)
f(2)=14
4a+2b+c=14(3)
Step 2
Eq.(1) + Eq(3)
8a+2c=8(4)
[2×Eq(2)]+Eq.(1)
6a+3c=0
c=2a(5)
From Eq.(4) and Eq.(5)
8a+2(2a)=8
4a=8
a=2
c=2×(2)=4
Now,from Eq.(2)
a+b+c=3
2+b+4=3
b=5
a=2,b=5,c=4
f(x)=2x25x+4
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Jeffrey Jordon
Answered 2022-01-30 Author has 2047 answers

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