So I assigned the classic fence-against-the-river question to my group (you have 200m of fencing, what's the largest rectangular area you can contain where one side is not needed against the river). We had just started quadratics so they have no real background in it at all. One student solved it thusly:
1) He made a table of values for a few fences:
Then, he turned to Maple. We had done a unit on linear systems and did a few questions on finding lines of best fit... so he used the Curve Fitting Tool to find the best fit parabola, then found the vertex of the parabola and hence the best area.
Then he found the vertex of the parabola by zooming:
Almost every other student did it the traditional way of setting up the equation, graphing and finding the vertex. I thought it was a nice bit of synthesis from the previous unit to approach it in this fashion!