Algebra

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Please help I can't figure out these two.

Express f(x) in the form a(x − h)2 + k.
f(x) = −4x2 + 24x − 9


Find the standard equation of a parabola that has a vertical axis and satisfies the given conditions.

vertex (0, −7), passing through (3, 38)

Thank You!

  • Algebra -

    for the first, complete the square:

    f(x) = -4(x^2 - 6x ......) - 9
    = -4( x^2 - 6x + 9 -9) - 9
    = -4( (x-3)^2 - 9) - 9
    = -4(x-3)^2 + 36 - 9
    = -4(x-3)^2 + 27

    for the second, you know the vertex is (0,-7)
    so f(x) = a(x-0)^2 - 7
    = ax^2 - 7
    but (3,38) lies on it, so
    38 = a(9)
    a = 38/9

    f(x) = (38/9)x^2 -7

  • Algebra -

    f(x) = -4(x^2-6x) - 9
    = -4(x^2-6x+9) -4(-9) - 9
    = -4(x-3)^2 + 27

    f(x) = a(x-0)^2 - 7
    38 = 9a-7
    a = 5
    f(x) = 5x^2 - 7

  • go with Steve's end # Algebra -

    don't know where my - 7 went ????

  • Algebra -

    Thank You Guys!!!

  • Algebra -

    F(x) = -4x^2+24x-9.

    h = -B/2A = -24/-8 = 3.
    k = -4*3^2 + 24*3 - 9=-36 + 72 - 9 = 27.

    F(x) = a(x-h)^2 + k.
    F(x) = -4(x-3)^2 + 27.

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