You can put this solution on YOUR website! To begin with, you can tell by looking at this that it is a parabola, since it has one variable squared but not the other. It opens either to the right or left because it has a . You can find the vertex by completing the square.
In order to make a perfect square trinomial on the left side of the equation, make sure you have a 1 for the coefficient of , then take half of the -12 (which is -6) and square it (which is 36), and add + 36 to each side of the equation:
Factor out the -4 on the right side:
Because the equation is in the form , it opens to the left. To find the vertex, you must "zero out" the x and the y portions of the equation which means that y = 6 and x = 8, or the vertex is at (8,6).
The graph should look like this parabola. (I don't know what is making what looks like a vertical line in the graph--that should NOT be there! Just the parabolic curve!!)
