Write the quadratic function g (x) = x^2 + 6x - 2 in vertex form and give the vertex

The vertex form of this equation is y = (x + 3) ^2 - 11

Step-by-step explanation:

In order to find the vertex form of the equation, we have to do a process called completing the square. The step by step instructions are below for you.

y = x^2 + 6x - 2

Add/Subtract the constant to the y side of the equation.

y + 2 = x^2 + 6x

Take half of the 6 coefficient (3) and then square it (9). Add that number to both sides.

y + 11 = x^2 + 6x + 9

Now you can factor the right side as a perfect square.

y + 11 = (x + 3) ^2

Lastly we add/subtract the constant back to the right side.

y = (x + 3) ^2 - 11