Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 2)3 + 8. The turning point of the graph is where the substance changes from a solid to a liquid. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.

Answer 1

For the answer to the question above, I will provide a solution like you requested so that it will give clarity to my answer.
T(x) = (x - 2)^3 + 8
T(x) = x^3 - 6x^2 + 12x
T(x) = 3x^2 - 12x + 12
Set that to zero:
3x^2 - 12x + 12 = 0
x^2 - 4x + 4 = 0
(x - 2)^2 = 0
x - 2 = 0
x = 2