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. 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

If I assume you meant


`-3(x-4)^(2)+10`

Then the answer is at 4 minutes. This is just the vertex form of the parabola which is


`y=a(x-h)^(2)+k`

where (h,k) is the vertex. h = 4 so the vertex is at 4 in the x-axis, or in the context of the problem it means at 4 minutes.