Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. 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

@Mehek

Answer 2

Im guessing T(x)=(x-4) * 3+6 since its next to the ()

Answer 3

so if im thinking correctly we first expand it?
(x-4)*3+6=3(x-4)+6

Answer 4

3(x-4)=3x-12

which makes it 3x-12+6

Answer 5

Subtract the numbers -12 + 6 = -6
making it 3x-6

Answer 6

Tx=3x-6
we then subtract 3x from both sides
Tx-3x=3x-6-3x

Answer 7

we then simplify
Tx-3x=-6

Answer 8

then we factor
Tx-3x=x(T-3)

Answer 9

x(T-3)=-6
Then divide by T-3;

Answer 10

\[\frac{ x(T-3) }{ T-3 }=\frac{ -6 }{ T-3 };\]

Answer 11

\[x=-\frac{ 6 }{ T-3}\]

Answer 12

\[T \neq 3\]

Answer 13

@Mehek am i correct?

Answer 14

Is it not T(x) = (x-4)^3 + 6?

Answer 15

Im stupid *smh* your right i misread it

Answer 16

UGHHHH i have to start over T~T

Answer 17

Which math are you taking

Answer 18

Algebra 2

Answer 19

(4,6) would be the vertex

Answer 20

Correct

Answer 21

So
The Turning Point of this Equation would be (4,6) i say this because when graphing this Equation the Degree is 3 meaning its a cubic function meaning it increases but also decreases leaving the vertex to be (4,6)

Answer 22

@Mehek would this be correct?

Answer 23

Yes