What is the vertex form of y= -6x^2 -27x-18?

Oct 11, 2017

$y = - 6 {\left(x + 2.25\right)}^{2} - 109.5$

Explanation:

Currently your equation is in standard form:

$y = a {x}^{2} + b x + c$ where $\left(- \frac{b}{2 a} , f \left(- \frac{b}{2 a}\right)\right)$ is the vertex

We want to put it in vertex form:

$y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right)$ is the vertex

We know $a = - 6$, but we have to figure out the vertex to find $h$ and $k$

$- \frac{b}{2 a} = - \frac{- 27}{2 \left(- 6\right)} = \left(\frac{27}{-} 12\right) = \left(- \frac{9}{4}\right) = - 2.25$

So:

$f \left(- 2.25\right) = - 6 {\left(- 2.25\right)}^{2} - 27 \left(- 2.25\right) - 18$

$= - 30.375 - 60.75 - 18 = - 109.5$

Thus our vertex is $\left(- 2.25 , - 109.5\right)$ and $h = - 2.25 , k = - 109.5$

Thus our equation is:

$y = - 6 {\left(x + 2.25\right)}^{2} - 109.5$