What is the vertex form of #y= 3x^2 + 9x-6#?

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Answer 1 · 2018-03-02T12:59:01

#3(x-3/2)^2-51/4#

The vertex form of the quadratic expression #ax^2+bx+c# is #a(x-h)^2+k#.

We have #3x^2+9x-6#

Or:

#3(x^2+3x)-6#

To complete the square, we take the coefficient of #3x#, divide it by #2#, square it and add it:

#3(x^2+3x+9/4)-6-27/4#

#3(x-3/2)^2-51/4#

So the vertex is, incidentally, #(3/2,-51/4)#