Answer:
(-4, -4)
Step-by-step explanation:
You have to put this in vertex form by completing the square in order to determine the vertex. Begin by setting the quadratic equal to 0 then moving the 12 over by subtraction:
[tex]x^2+8x=-12[/tex]
The rules are to take half the linear term, square it, and add it to both sides. Our linear term is 8. Half of 8 is 4, and 4 squared is 16. So we add 16 to both sides:
[tex](x^2+8x+16)=-12+16[/tex]
During this process we have created a perfect square biomial on the left. We will state that, along with simplifying on the right:
[tex](x+4)^2=4[/tex]
Now we will move the 4 back over and set it back to equal y:
[tex](x+4)^2-4=y[/tex]
And from this you can see that the coordinates of the vertex are (-4, -4)
