## 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

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## Answers ( )

f(x) = 2 -4x

Step-by-step explanation:Step 1 :Given, f(x) = a(x – h)2 + k

Point on the parabola is (3, 6)

Vertex (h,k) = (1,-2)

Step 2:Substituting the vertex in the equation we have,

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

Substituting the point (3,6) in this we have,

6 = a(3-1)2 – 2 => 6 = 4a -2

=> 4a = 8 =>

a = 2Step 3 :Substituting the value for a and the vertex in the given equation we have

f(x) = 2(x-1)2 -2 = 2(x2 – 2x + 1) -2 = 2×2 – 4x

=> f(x) = 2 -4x which is the standard form