# How do you find the vertex of g(x)=3x^2-24x-110?

Oct 24, 2016

THe vertex is at (4,-158)

#### Explanation:

$g \left(x\right) = 3 {x}^{2} - 24 x - 110$
we complete the square

$g \left(x\right) = 3 \left({x}^{2} - 8 x\right) - 110$

$g \left(x\right) = 3 \left({x}^{2} - 8 x + 16\right) - 110 - 48$

We factorise
$g \left(x\right) = 3 {\left(x - 4\right)}^{2} - 158$

So the vertex is when $x = 4$$\implies$y=-158#