# 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

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

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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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