Question

Based on experimental data, the function T(x) = -3(x − 4)^3 + 10 models the temperature of a special substance after being placed in a freezer for x minutes . The turning point of the graph marks the moment when the substance changes from a liquid to a solid. Explain. Thanks!

Answer 1

I can't say for sure this answer is 100% correct because I think more info is needed.

If your teacher is looking for the turning point, then that would be (4,10)

The equation y = a(x-h)^3 + k has a turning point at (h,k). The parent function y = x^3 gets shifted h units to the right (assuming h is positive) and k units up (if k is positive). In this case, (h,k) = (4,10) so we have y = a(x-4)^3 + 10. The original turning point (0,0) has been shifted to the new turning point (4,10) which is 4 units to the right and 10 units up. The value of 'a' does not effect the turning point.

If x was say the time in minutes and y was the temperature, then the turning point of y = -3(x-4)^3 + 10 could mean that at time 4 minutes (x = 4) the substance turns from liquid to solid (y = 10 degrees).

Note: more information is needed about this function be 100% certain about the claim made.