Select the correct vertex form of the following equation y=x2+6x-9

1 answer

The vertex form of the equation y=x^2+6x-9 can be found by completing the square.

First, we group the first two terms together and leave the constant term separate:

y = (x^2 + 6x) - 9

Next, we need to complete the square by adding and subtracting a constant, which is half the coefficient of the x term squared. In this case, that constant is (6/2)^2 = 9.

y = (x^2 + 6x + 9 - 9) - 9

We can rewrite the first three terms as a perfect square trinomial:

y = (x+3)^2 - 9 - 9

Finally, we combine the constant terms:

y = (x+3)^2 - 18

Therefore, the correct vertex form of the equation is y = (x+3)^2 - 18.