I am confused on a problem I have in algebra two that is below.
A bottom for a box can be made by cutting congruent squares from each of the four corners of a piece of cardboard. Write an expression for the volume of the box that could be made from a $7$ by $10$ piece of cardboard. Using a graphing calculator, find the maximum volume for your box to the nearest hundredth.
So, I believe that the equation would be $(10-2x)(7-2x)(x)$ in factored form and $4x^3-34x^2+70$ in standard form. I do not however own a graphing calculator and cannot find the last part of the problem. I have tried going to desmos, however I cannot find a maximum with that equation. If anyone is able to help that would be very much appreciated.
You're on the right track! Your factored form is indeed correct, but the standard form is just a bit off: $$\begin{align}(10-2x)(7-2x)(x)&=(4x^2-14x-20x+70)(x)\\&=x(4x^2-34x+70)\\&=4x^3-34x^2+70x\end{align}$$
If you look at the Desmos graph I've made here, you can see that the graph of $y=4x^3-34x^2+70x$ has a maximum at the point $(1.35,42.38)$, so your answer would be $42.38\ \text{(units)}^3$.