Which of the following are the coordinates of the vertex of y=x^2 + 12x-9

So for this, you will be converting this standard form equation to vertex form, which is y = a(x - h)^2 + k.

So firstly, put x^2 + 12x into parentheses: y = (x^2 + 12x) - 9

Next, you want to make what is inside the parentheses a perfect square. To do that, you need to divide the x coefficient by 2 and then square that result. In this case, the quantity is 36. Add 36 into the parentheses and subtract 36 outside the parentheses: y = (x^2 + 12x + 36) - 9 - 36

Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is y = (x + 6)^2 - 45

Now from the vertex form (y = a(x - h)^2 + k) , the vertex is going to be (h,k). Looking at our equation, the vertex is (-6, -45) (remember that (x + 6) is the same as (x - (-6))