Question

What is the equation, in standard form, of a parabola that models the values in the table?
x –2 0 4
ƒ(x) 1 5 -59

Answer 1

ax^2 + bx + c = 1
plug in first value
4a -2b + c = 1

do the same for the others:

0 + 0 + c = 5
c = 5

16a + 4b + c = -59

so we plug in c into the equations with and b:

16a + 4b + 5 = -59
4a -2b + 5 = 1

4a = 2b -4
2a = b - 2

16a + 4b = -64
8(b-2) + 4b = -64

2(b-2) + b = -16
2b - 4 + b = -16
3b = -12
b = -4
Plug in for a
2a = -4 - 2
2a = -6
a = -3

So the equation is:
-3x^2 - 4x + 5