Question

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



x –2 0 4
f(x) 1 5 –59

Answer 1

y = ax^2 + bx + c
we must replace each pair of values and form equations

Answer 2

1 = a(-2)^2 + b(-2) + c
5 = a(0)^2 + b(0) + c
_59 = a(4)^2 + b(4) + c

Answer 3

from the second equation c = 5
then
1 = 4a - 2b + 5 ---------> 4a - 2b = -4 ( 1)
-59 = 16a + 4b + 5 -------> 16a + 4b = -64 (2)

we solve multiply (1) by 2 8a - 4b = -8
16a + 4b = -64

We add (1) + (2)
24a = -72 ---------> a = -3

then we replace "a" in (1) 4(-3) - 2b = -4
-12 -2b = -4
-12 + 4 = 2b
-8 = 2b
b = -4

Answer 4

Finally y = -3x^2 -4x + 5

Answer 5

It was a pleasure to help you

Answer 6

thanks!