# What is the vertex of  y=-3x^2 -4x-2?

Aug 16, 2017

The vertex is $\left(- \frac{2}{3} , - \frac{2}{3}\right)$.

#### Explanation:

This equation is currently in standard form and you must convert it to vertex form to figure out the vertex.

Vertex form is usually written as $y = a {\left(x - h\right)}^{2} + k$, where the point (h,k) is the vertex.

To convert, we can use the process of completing the square.

First, we pull out the negative 3.

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

In completing the square, you take half of the coefficient on the x term (4/3 here), square it, and add that into the problem. Since you are adding a value, you must also subtract the same value so as not to change the equation.

$y = - 3 \left({x}^{2} + \frac{4}{3} x + \frac{4}{9}\right) - 2 + \frac{4}{3}$

Now it looks like I added in 4/9 and added 4/3, but you have to be careful. Because of the -3 in front of the parentheses, when I put in 4/9, it's really like I am subtracting 4/3. Thus, I must do the opposite to keep the equation the same, so I added 4/3 at the end.

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

I factored the binomial to simplify, and now I have the equation in the proper vertex form. The vertex is point (h,k) but because h is supposed to be subtracted from x, I need to flip the sign on the positive 2/3, giving us the point $\left(- \frac{2}{3} , - \frac{2}{3}\right)$.