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?

in progress 0
Reagan 2 weeks 2021-11-23T22:39:04+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-23T22:40:44+00:00

    f(x) = 2 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 = 2

    Step 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 x^{2} -4x  which is the standard form

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )