Question

What is the equation, in standard form, of a parabola that models the values in the table?

Answer 1

f(x) = ax^2 + bx + c

f(0) = ax^2 + bx + c = 5, c = 5
f(-2) = 4a + -2b + 5 = 1 ----------(1)
f(4) =16a + 4b + 5 = -59 ----------(2)
4a -2b = -4
16a + 4b = -64 
16a + 4(-2-2a)= -64
16a - 8 - 8a = -64
8a = -56
a = 7
4a - 2b = -4 
28 - 2b = -4
b = 16

f(x) = 7x^2 + 16x + 5