Question

How do you graph `y<x^2-3x`?

Answer 1

graph{y<(x^2-3x) [-10.5, 9.5, -4.8, 5.2]}

Explanation:

First, we know it will look like an upward-facing parabola because of the first term in the function `x^2` with a coefficient of positive one.

Next we can determine that the graph will be shaded everywhere below the parabola, and the parabola will be a dotted line because of the `<` sign.

Now, we find where the dotted upward facing parabola has a vertex and where its intercepts are. I'm going to write this using an equals sign rather than a less than symbol, because we are only looking for where the parabola is right now.

`y=x^2-3x`
`y=(x)(x-3)`
Roots are at `x=0` and `x=3`
`y=x^2-3x`
`y=(x-1.5)^2-2.25`
Vertex is at `(1.5,-2.25)`