What is the correct answer?

Question

A quadratic function has a vertex point of (3, 1) and passes through the point (6, -8). Write the equation in standard form that represents the quadratic function.

A.f(x)=(x+6)² -8

B.f(x)=x²−12x+28

C.f(x)=(x+1)²−3

D.f(x)=x²−2x+4

Answer 1

f(x) = a(x - h)² + k

f(x) = a(x - 3)² + 1

-8 = a(6 - 3)² + 1

-8 = 9a + 1

-9 = 9a

-1 = a

f(x) = -(x - 3)² + 1

Answer 2

Starting off with the vertex form of a parabola, f (x) = a(x - h)² + k, where (h, k) is the vertex. Plugging in the vertex given.

f (x) = a(x - 3)² + 1 Now plug in the point given and solve for a

-8 = a(6 - 3)² + 1 Simplify

-8 = a(3)² + 1 Simplify

-8=9a+1 Subtract 1 from both sides

-8-1=9a+1-1 SImplify

-9=9a Divide both sides by 9

a=-1 Plug this into the equation

f (x) = -(x - 3)² + 1 FOIL

f (x) = -(x - 3)(x - 3) + 1

f (x) = -(x²-6x+9) +1 Distribute

f (x) = -x²+6x-9 +1 Combine like terms

f (x) = -x²+6x-8

I don't believe that any of the choices you are showing are correct. A and C are not in standard form. The others do not match.