# How do you write the quadratic in vertex form given y=3x^2+6x-1?

May 9, 2015

The vertex form is:

$y - {y}_{v} = a {\left(x - {x}_{v}\right)}^{2}$.

So:

$y = 3 \left({x}^{2} + 2 x\right) - 1 \Rightarrow y = 3 \left({x}^{2} + 2 x + 1 - 1\right) - 1 \Rightarrow$

$y = 3 \left({x}^{2} + 2 x + 1\right) - 3 - 1 \Rightarrow y = 3 {\left(x + 1\right)}^{2} - 4 \Rightarrow$

$y + 4 = 3 {\left(x + 1\right)}^{2}$.