## Find the equation f(x) = a(x – h)2 + k for a parabola containing point (3, 6) and having (1, -2) as a vertex. What is the standard form of t

Question

Find the equation f(x) = a(x – h)2 + k for a parabola containing point (3, 6) and having (1, -2) as a vertex. What is the standard form of the equation?
A) The vertex form is f(x) = 2(x – 1)2 − 2. The standard form is f(x) = 2×2−4x.
B) The vertex form is f(x) = 2(x + 1)2 + 2. The standard form is f(x) = −2×2−4x.
C) The vertex form is f(x) = −2(x – 7)2− 2. The standard form is f(x) = 2×2 + 4x.
D) The vertex form is f(x) = −2(x – 1)2 − 2. The standard form is f(x) = 2×2 +4 x.

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1. the 1 is the h and the -2 is the k

f(x) = a(x – h)^2 + k

f(x) = a(x-1)^2 -2

to find a  substitute x=3, y=6 in

6= a(3-1)^2 -2

6 =a *2^2 -2

8 = 4a

a =2

f(x) = 2(x-1)^2 -2  this is the vertex form

distribute to get the standard from

f(x) = 2(x^2-2x+1) -2

2x^2 -4x+2-2

f(x) =2x^2-4x   is the standard form

Choice A

2. for form , the vertex is (h,k)

given that the vertex is (1,-2), h=1, k=-2 find a by subsituting the given point

(3,6), x=3 and f(x)=6         vertex form is standard form is 