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))

The coordinates of the vertex are (-6, - 45).

We can find the vertex by using the formula for finding x-coordinates. The formula for the x-coordinate of a vertex is below.

-b/2a

In this equation, a is the coefficient of the x^2 term (1) and b is the coefficient of the x term (12). Then we can plug in to find the x term.

- (12) / 2 (1)

-12/2

-6

Now that we have this term, we can plug it in for all values of x to find the y term.

x^2 + 12x - 9

-6^2 + 12 (-6) - 9

36 - 72 - 9

-45