Question

How do you graph the function `y=5x-x^2`?

Answer 1

graph{5x-x^2 [-14.24, 14.23, -7.12, 7.12]}

First you realise that `5x-x^2=x(5-x)` which will give the
`y=0` solutions `x=0` and `x=5` for `(0,0)` and `(5,0)`

Then, put the halfway-`x` (`2.5`) in the equation to get the top of the graph `y=5*2.5-2.5^2=6.25` for `(2.5,6.25)`

You now have the three most important points of your graph. You can put more `x`-values in, of course, so you get more points, but these three are essential.