Question

Find the vertex of the parabola whose equation is y = x 2 + 8x + 12.

Answer 1

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:

$x^2+8x=-12$

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:

$(x^2+8x+16)=-12+16$

During this process we have created a perfect square biomial on the left. We will state that, along with simplifying on the right:

$(x+4)^2=4$

Now we will move the 4 back over and set it back to equal y:

$(x+4)^2-4=y$

And from this you can see that the coordinates of the vertex are (-4, -4)