Algebra HW?

Question

How do we do these?

Determine whether a quadratic model exists for each of values. If so, write the model.
A. f(0) = 5, f(20 = 3, f(-1) = 0

Dont they need like a ^2 to be quadratic?

Answer 1

Assume a model of form

f(x) = ax² + bx + c where a, b, and c are constants.

5 = f(0) = a*0² + b*0 + c so c = 5

So

f(x) = ax² + bx + 5

3 = f(2) = 4a + 2b + 5 so
4a + 2b = -2

0 = f(-1) = a - b + 5 so
a - b = -5

Solve 4a + 2b = -2 and a - b = -5 simultaneously to find a and b. You should get a = -2, b = 3, so

f(x) = -2x² + 3x + 5

Check:

f(0) = -2*0² + 3*0 + 5 = 5
f(2) = -2*2² + 3*2 + 5 = 3
f(-1) = -2*(-1)² + 3*(-1) + 5 = 0