SOLUTION: Eliana wants to make a diorama or an art contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby

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Question 1120778: Eliana wants to make a diorama or an art contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open front.

Write the function v(x)=(12-2x)(8-2x)x in factored form.
Select all the following that are true. Explain your reasoning.
A. V(x)=(12-2x)(8-2x)x
B. V(x)=4x(6-x)(4-x)
C. V(x)=-4x(x-6)(x-4)
D. The zeros of y=v(x) correspond to the values of x that result in a diorama box with volume in 36 in^3.
E. The graph of y=v(x) crosses the x-axis at (0,0), (4,0), and (6,0)
F. The graph of y=v(x) shows that there is only one value of x for which the volume of the diorama box will be in 36in^3.
G. The graph of y=v(x) has a turning point between x=0 and x=4.
H. The only portion of the graph that represents the possible volumes of Eliana's diorama box is the portion for which 0 < x <4.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


C is false because and , so factoring out -1 from each of the binomial factors would result in:



D is false because the function is a volume function. That is the value of the function IS the volume. So a zero of the VOLUME function is a place where the VOLUME is ZERO.

F is false. Draw a line at y = 36 across your graph.

The rest is true.


John

My calculator said it, I believe it, that settles it