Question

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

x -1, 0, 2

f(x) 12, 5, 15

Answer 1

y = a x^2 + b x + c

12 = a (1) + b(-1) + c
5 = a(0) + b(0) + c so c = 5
15 = a(4) + b(2) + 5

7 = a - b so a = b + 7
10 = 4 a + 2 b

10 = 4(b+7) + 2 b
10 = 4 b + 28 + 2 b
6 b = -18
b = -3 then a = b+7 = +4
so
y = 4 x^2 - 3 x + 5

Answer 2

Thank you very much good sir!

Answer 3

You are welcome.