What is the vertex form of 4x^2+4x-12

(-1/2, -13/4)

Step-by-step explanation:

Start with y = 4x^2+4x-12.  Put this into the form y = a(x-h)^2 + k, where (h, k) represents the vertex.

Factor 4 out of this expression, obtaining:  y = 4(x^2 + x - 3).

Next, complete the square of the quantity inside parentheses:

y = 4[ x^2 + x + 1/4 - 1/4 - 3 ], or

y  = 4[ (x + 1/2)^2 - 13/4 ]

We can now conclude that the vertex is (-1/2, -13/4).

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