What is the vertex of #y=2(x +3)^2 -8x #?

1 Answer
Topscooter
Dec 21, 2015

The vertex is #(-1,16)#.

Explanation:

In order to know, we will develop first, it will make the next calculus easier.

#y = 2x^2 + 12x + 18 - 8x = 2x^2 + 4x + 18#. The coefficient of #x^2# is positive so we know the vertex is a minimum. This vertex will be the zero of the derivative of this trinomial. So we need its derivative.

#f(x) = 2x^2 + 4x + 18# so #f'(x) = 4x + 4 = 4(x+1)#. This derivative is zero for #x = -1# so the vertex is at the point #(-1,f(-1)) = (-1,16)#

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