Question

Use a system of equations to find the quadratic function

f(x) = ax^2+ bx + c
that satisfies the equations. Solve the system using matrices.

f(1) = 3, f(2) = 12, f(3) = 25

Answer 1

Answer:
`f(x)=2x^(2) +3x-2`

Explanation:

f
`f(1)=3\\\\ax^(2) +b+c=3 (1)\\f(2)=12\\4a+2b+c=12 (2)\\f(3)=25\\9a+3b+c=25(3)\\(2)-(1)= 3a+b=9 (4)\\(3)-(2)=5a+b=13 (5)\\(5)-(4)= > 2a=4 = > a=2\\(4)= > b=3\\(1)= > c=-2\\f(x)=2x^(2) +3x-2`