What is the domain of this function?

[bully3000]

An open topped box is to be made by cutting out identical squares from the corners of a rectangular piece of cardboard then folding up the resulting flaps. Thus, if the side of each removed square has length x then the box height will also be x. If the cardboard has dimensions 50cm by 40cm find an expression for the volume of the box V(x) in terms of x. What is the domain of this function? What sort of function is it (quadratic, cubic or...?)

Any help will be appreciated!

[brightsky]

so you have a rectangular piece of cardboard with dimensions 50*40 cm to start with. you cut out identical squares with dimensions x*x from the fourt corners of the piece of cardboard. the dimensions of the open topped box thus obtained would be (50-2x)*(40-2x)*x.

so V(x) = x(50-2x)(40-2x)
we know that x>0, 50-2x>0, 40-2x>0 or else we would not get a box. solving these 3 inequations simultaneously yields an implied domain of 0<x<20.

[bully3000]

so you have a rectangular piece of cardboard with dimensions 50*40 cm to start with. you cut out identical squares with dimensions x*x from the fourt corners of the piece of cardboard. the dimensions of the open topped box thus obtained would be (50-2x)*(40-2x)*x.

so V(x) = x(50-2x)(40-2x)
we know that x>0, 50-2x>0, 40-2x>0 or else we would not get a box. solving these 3 inequations simultaneously yields an implied domain of 0<x<20.

What sort of function is it though?

I tried graphing it on my cas but it says "invalid implied multiply" after I try to...

[Jeggz]

It would be a cubic graph 

[bully3000]

thought so but wanted to check with u guys just in case...