Math

Find the vertex of the parabola.
y = -4x2 - 16x - 11

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  1. y = -4x^2 - 16x - 11
    there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x:
    y = -4x^2 - 16x - 11
    y' = -8x - 16
    then we equate this to zero (because vertex is a maximum or a minimum and therefore the slope is zero):
    0 = -8x - 16
    8x = -16
    x = -2
    substitute this back to the original given equation:
    y = -4x^2 - 16x - 11
    y = -4(-2)^2 - 16(-2) - 11
    y = -16 + 32 -11
    y = 5
    therefore vertex is at
    (-2, 5)

    hope this helps~ :)

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  2. If you don't know Calculus, like in Jai's method,
    then....

    the x value of the vertex is -b/(2a) = 16/-8 = -2
    sub into original to get
    y = -16 + 32 - 11 = 5

    vertex is (-2,5)

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