So if the graph is of (-1, -4.5), I do notice that -1/2 * (3^2) = -4.5. If there was a calculator involved, I could imagine a student typing 3sqrt(-1) instead of cube root, and then getting a calculator error. Maybe after 3sqrt(-1) didn’t work they thought that “negative exponents flip the fraction, and square root = 1/2 for the exponent” and turned 3sqrt(-1) into 3^2? But wouldn’t 3*(1^2) = 3 been more likely? Or if they weren’t using a calculator anymore since they got the error, why not 1^3?

Did the student use a calculator? Was this mistake consistent with how they graphed (0,0) and (1,1/2)? What happened on the following question? Was it consistent?