Iam a bit confused on this one, not really sure where to go with it other than the fact that you change t(x) to zero

in your lab, a substance's temperature has been observed to follow the function t(x) = (x + 5)3 + 7. the turning point of the graph is where 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.

What your teacher wanted you to do was to find where the equation equaled zero
I have no idea why she would want yu do to that though because the turning point on the graph would be the vertex, not the zeroes of the graph

using math we do math stuff
this equation is 3rd degree
T(x)=(x+5)^3+7
I hope you meant (x+5)^2+7, because then the answer would be at (-5,7)

if yo meant 3rd degree then here wer go with calculus and deritivives

take the derivieve and find where the slope is 0
T'(x)=3(x+5)^2
where it is equal 0 is wehre x=-5
use sign chart
it is positive at both places
no turning point

well, dunno

if it was 2nd degree euation then vertex or turning point would be at (-5,7)