Checking a sketch

Is it possible to check a sketch for correctness in the following way:

I would like students to draw an arrows in QI and QIII, (to show the end behavior of a polynomial). Is there a way to check that they student has sketched in only those quadrants and not the others?

You could check the y-values at a specific x-value to test the behavior.

numberList("Y_{right}"): this.sketch.xValuesAt(9)
numberList("Y_{left}"): this.sketch.xValuesAt(-9)

That will give you two lists you can play with in the calculator. Then to make sure that you are in Q1 and Q3 you would need to make sure that min(Y_{right})>0 and max(Y_{left})<0.

Another option is making a draggable arrow in a graph. Graphing Calculator