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

Nov 15, 2016

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.

$y = {x}^{2} - 3 x$
$y = \left(x\right) \left(x - 3\right)$
Roots are at $x = 0$ and $x = 3$
$y = {x}^{2} - 3 x$
$y = {\left(x - 1.5\right)}^{2} - 2.25$
Vertex is at $\left(1.5 , - 2.25\right)$