Complete the square to re-write the quadratic function in vertex form:y, equals, x, squared, plus, 6, x, plus, 7y=x 2 +6x+7

Sure, let's complete the square to rewrite the quadratic function in vertex form.

Given the quadratic function: $y = x^2 + 6x + 7$

Step 1: Start with the quadratic and linear terms. $y = x^2 + 6x + 7$

Step 2: To complete the square, we need to add and subtract the same value inside the equation. Take the coefficient of $x$, which is 6, divide it by 2, and then square it. $\left(\frac{6}{2}\right)^2 = 3^2 = 9$

Step 3: Add and subtract this value (9) inside the equation. $y = x^2 + 6x + 9 - 9 + 7$

Step 4: Rewrite the quadratic and linear terms as a perfect square trinomial. $y = (x^2 + 6x + 9) - 9 + 7$

Step 5: Simplify the equation. $y = (x + 3)^2 - 2$

So, the quadratic function in vertex form is: $y = (x + 3)^2 - 2$