Use a system of equations to find the quadratic function f(x) = ax^2 + bx + c

Question

that satisfies the equations. Solve the system using matrices.
f(−2) = 4, f(1) = −2, f(2) = −12

The answer i got is f(x)=-2x^2-4x+8

this is the steps of how i got f(x)=-2x^2-4x+8
(x) = ax^2 + bx + c
form the equations, using the 3 given points.
4a - 2b + c = 4
a + b + c = -2
4a + 2b + c = -12

These are too easy to complicate things with matrices
subtract the first two:
3a -3b = 6
a - b = 2

subtract the last two
3a + b = -10
add these two :
4a = -8
a = -2

3(-2)+b=-10
-6+b=-10
b=-10+6
b=-4

a+b+c=2
(-2)+(-4)+c=2
-6+c=2
c=2+6
c=8

.˙. a= -2, b=-4, c=8:
f(x)=-2x^2-4x+8

Answer 1

can someone check my answer please

Answer 2

I am assuming you are the student that had:
https://www.jiskha.com/questions/1791127/Use-a-system-of-equations-to-find-the-quadratic-function-f-x-ax-2-bx-c-that
and I agree with your final steps.

You could test if you are correct by simply subbing in the given points and make sure they satisfy the equation. They do.

Answer 3

i am that student on that website. while i was waiting for someone to response back, i subbed the numbers in and the equation f(x)=-2x^2-4x+8 is wrong. What do i do now???

Answer 4

Your given points were:
(-2,4), (1,-2) and (2,4)
I had started you off and I let you finish the solution after I found a = -2
you correctly had b = -4, but c should have been 4, not 8 like you have.
I noticed that my equation was a+b+c = -2
you had a+b+c = 2

the equation is f(x) = -2x^2 - 4x + 4

and the points work in that equation.

Answer 5

it works and it is correct