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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Answers ( No )

    0
    2021-09-09T01:05:38+00:00

    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

    add 2 to each side

    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

    0
    2021-09-09T01:05:53+00:00

    for form f(x)=a(x-h)^2+k, the vertex is (h,k)

    given that the vertex is (1,-2), h=1, k=-2

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

    find a by subsituting the given point

    (3,6), x=3 and f(x)=6

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

    6=a(2)^2-2

    6=4a-2

    8=4a

    2=a

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

    epxnad to find standard form

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

    f(x)=2x^2-4x+2-2

    f(x)=2x^2-4x

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

    standard form is f(x)=2x^2-4x

    answer is A

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