What is the vertex form for y = x^2 + 8x - 1

The vertex form of this equation is y = (x + 4) ^2 - 17

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 + 8x - 1

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

y + 1 = x^2 + 8x

Take half of the 8 coefficient (4) and then square it (16). Add that number to both sides.

y + 17 = x^2 + 8x + 16

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

y + 17 = (x + 4) ^2

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

y = (x + 4) ^2 - 17