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.

The turning point of the function is

(x,T(x)) = (2, 8)

Step-by-step explanation:

Since we have an explicit representation of the process, given by the equation T(x), we can easily know what is going with the experiment if we plot T(x) using any graphing calculator or tool.

Please see attached image.

We know that the vertex of a quadratic equation is the maximum or minimum point of the function.

If we look at the graph, concavity changes exactly at x =2

T(x) = (x − 2)^3 + 8

T(x) = (2 − 2)^3 + 8

T(x) =  8

the answer to the question is a  

it has the same slope and the same y-intercept.