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identify the vertex of the parabola y=4x2-40x+96

  • Math ( not J&W) -

    several ways to do this.

    quickest way:
    the x of the vertex is -b/(2a)
    = -(-40)/8 = 5
    sub back into equation
    y = 4(25) -40(5) + 96 = -4

    vertex (5,-4)

    calculus way:
    dy/dx = 8x - 40 = 0
    x = 5
    proceed as above

    completing the square:
    y = 4x^2 - 40x + 96
    = 4(x^2 - 10x + 25 - 25 + 96
    = 4((x-5)^2 - 25) + 96
    = 4(x-5)^2 - 100 + 96
    =4(x-5)^2 - 4

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