Use a system of linear equations to find the quadratic

Lloyd Allen

Lloyd Allen

Answered question

2021-12-05

Use a system of linear equations to find the quadratic function
f(x)=ax2+bx+c
that satisfies the given conditions. Solve the system using matrices.
f(2)=6, f(1)=3, f(2)=14
f(x)=?

Answer & Explanation

juniorekze

juniorekze

Beginner2021-12-06Added 18 answers

Step 1
Given,
f(x)=ax2+bx+c
f(2)=6, f(1)=3, f(2)=14
f(2)=6
1) 4a2b+c=6
f(1)=3
2) a+b+c=3
f(2)=14
3) 4a2bc=14
Step 2
Eq. (1) + Eq. (3)
4) 8a+2c=8
[2×Eq.(2)]+Eq.(1)
6a+3c=0
5) c=2a
From Eq. (4) and (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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