Question

1. Write a function V(x) that models the volume of the box where the length of the sides of the squares is x cm. (The formula for the volume of a box is: V = l ⋅ w ⋅ ℎ).2. Graph V(x). (You may use Desmos or draw in the provided grid.)

Answer 1

From the problem, the length and the width will be reduced by twice the side of the square.

The length of the box will be :

$26-2x$

The width of the box will be :

$20-2x$

and the height will be the measurement of the square side :

$x$

Note that the volume of a box is length x width x height.

1. The volume will be :

$V(x)=x(26-2x)(20-2x)$

Expand and simplify the function :

$\begin{gathered} V(x)=x(26-2x)(20-2x) \\ V(x)=x(520-40x-52x+4x^2) \\ V(x)=x(4x^2-92x+520) \\ V(x)=4x^3-92x^2+520x \end{gathered}$

2. Graph the function using desmos.

Answer 2

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