I'm having problems with this problem...
"A rectangle has its base on the X-axis, and its upper two vertices lie on the parabola y=12-x^2. What is the largest area the rectangle can have? What are the dimensions?"

I've gotten this far...
Area= Length * Width
Length= 2X (cuz X can't go into the negatives, right?) * width
y=12-x^2
A=2x*(12-x^2)
Any time I try to graph it to see the Maximum, I see nothing.

Am I even on the right track?

Yes, you're on the right rack. Are you graphing throughout the full domain for x from 0 to sqrt(12)? When you graph it, you're a function should look like the attached. Note there's a definite maximum.

Oh! Thank you so much!! I think I put it in wrong! So would the area be 32, and the dimensions be 2*32?

Almost right - yes, the area is 32, and the max occurs when x = 2, but that makes the dimensions 4*8.