# How do you find the vertex of y = 3x^2 -6x-4?

Jul 15, 2015

Convert to vertex form to obtain the vertex at $\left(1 , - 7\right)$

#### Explanation:

The easiest way to solve this requirement is to rewrite the equation into vertex form:
$\textcolor{w h i t e}{\text{XXXX}}$$y = m {\left(x - a\right)}^{2} + b$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$which will have a vertex at $\left(a , b\right)$

Given $y = 3 {x}^{2} - 6 x - 4$

Extract $m$
$\textcolor{w h i t e}{\text{XXXX}}$$y = 3 \left({x}^{2} - 2 x\right) - 4$

Complete the square by adding $3 \left(1\right)$ and then subtracting $3$ as
$\textcolor{w h i t e}{\text{XXXX}}$$y = 3 \left({x}^{2} - 2 x + 1\right) - 4 - 3$

Rewrite as a squared binomial and simply
$\textcolor{w h i t e}{\text{XXXX}}$$y = 3 {\left(x - 1\right)}^{2} + \left(- 7\right)$

Since this is in vertex form, we can simply read the vertex off as:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(1 , - 7\right)$