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. (10 points). Please help

Answer 1

The turning point is (2,8)

Explanation:

we know that

The general equation of the substance's temperature is equal to

`T(x)=(x-h)^(3)+k`

where

(h,k) is the vertex (turning point)

In this problem we have

`T(x)=(x-2)^(3)+8`

so

(h,k)=(2,8)

therefore

The turning point is (2,8)