Find a quadratic model for the set of values

Question

(-2,8)(0,-4)(4,68)

Answer choices:

A.y=4x^2+2x-4

B.y=2x^2+4x-4

C. y=-4x^2-2x+4

Answer 1

I assume you're not supposed to just use trial and error...

The general form is Ax^2 + Bx + C. You have 3 unknowns, so you need 3 equations. That can be done using the given points.

(-2,8)(0,-4)(4,68)

Easy one first: If x = 0, the first 2 terms drop out, leaving us with C = -4

Now we just need 2 equations. Write each one with one of the remaining given points, and entering -4 for C:

A(-2)^2 + B(-2) - 4 = 8

A(4)^2 + B(4) -4 = 68

4A - 2B = 12

16A + 4B = 72

Solve this pair of equations and you'll have A and B