Question

The area, A, in square feet, of a rectangular storage bin in a warehouse is given by the function A(x) = x2 - 6x, where x is the width, in feet, of the storage bin.

Part A: Based upon this function, which statement would be true? Show your work or explain how you found the solution.


The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the length of the storage bin.


The x-intercepts of the function are 3 and -9, which are a lower bound and an upper bound for the possible values of the width of the storage bin.


The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the length of the storage bin.


The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.

Answer 1

The x-intercepts of the function are 0 and 6, which are a lower bound and an upper bound for the possible values of the width of the storage bin.

Explanation:

Given

`A(x) = x^2 - 6x`

Required

Which is true about the x intercept

To do this, we make A(x) = 0.

Substitute 0 for A(x) in
`A(x) = x^2 - 6x`

`0 = x^2 - 6x`

Rewrite as:

`x^2 - 6x=0`

Factorize:

`x(x - 6)=0`

Split:

`x = 0\ or\ x - 6 = 0`

`x = 0\ or\ x = 6`

Option D is correct