Mathematics

What value of x will give the minimum value for 9x^2 + 18x + 7?

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  1. y = 9x^2 + 18x + 7
    IF you do calculus:
    slope = dy /dx = 18 x + 18
    where is it zero?
    18 x = - 18
    x = -1
    IF you do algebra:
    y = 9x^2 + 18x + 7
    9 x^2 + 18 x = y-7
    x^2 + 2x = (y-7)/9
    x^2 + 2 x + 1 = (y-7)/9 + 9/9
    (x+1)^2 = (1/9)(y +2/9)
    vertex at x = -1

  2. typo
    x+1)^2 = (1/9)(y + 2)
    vertex at x = -1

  3. Y = 9x^2+18x+7
    h = Xv = -B/2A = -18/18 = -1.
    So X = -1 gives minimum value of the Eq. :
    Y min. = 9*(-1)^2+18*(-1)+7 = -2 = min. value of Eq.

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