Select the correct vertex form of the following equation. show all your work

Question

y=x2+6x−9

answer : y=(x−3)^2−4

Answer 1

To convert the given equation into vertex form, we need to complete the square.

First, let's group the terms:
y = x^2 + 6x - 9

Next, we want to add and subtract a constant inside the parentheses to complete the square. To determine the constant, take half of the coefficient of x and square it. In this case, half of 6 is 3, and 3 squared is 9.

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

Now, we can rewrite the equation as:
y = (x^2 + 6x + 9) - 9 - 9

Now, let's factor the square trinomial in the parentheses:
y = (x + 3)^2 - 18

Simplifying further, we have:
y = (x + 3)^2 - 18

Therefore, the correct vertex form of the equation is y = (x - 3)^2 - 4.