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

1 Answer
Aug 16, 2017

The vertex is #(-2/3, -2/3)#.


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(x-h)^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.


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.


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.


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 #(-2/3, -2/3)#.