Question

A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the graph of this polynomial equals which of the following? Choose all that apply.

Answer 1

The maximum length (x) of the rectangular box

The minimum volume (y) of the rectangular box

The minimum height (8-x) of the rectangular box

Explanation:

we have

`y=3x(8-x)`

This is the equation of a vertical parabola open downward

The vertex is a maximum

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The x-intercepts of the equation are

(0,0) and (8,0)

therefore

The greatest x-intercept is the point (8,0)

see the attached figure

Remember that x represent the length of the box

therefore

The greatest x-intercept of the graph of this polynomial equals to

The maximum length (x) of the rectangular box

The minimum volume (y) of the rectangular box

The minimum height (8-x) of the rectangular box