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(−2) = 4, f(1) = −2, f(2) = −12

Answer 1

f(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

sub back into 3a+b=-10 to get b
then sub back into a + b + c = -2 to get your c