# How do you graph y<x^2?

Apr 3, 2015

Well, first of all consider the associated equation $y = {x}^{2}$. It's the well-known parabola:

graph{x^2 [-10.17, 9.83, -1.88, 8.12]}

But the graph in blue is nothing but the set
$\left\{\left(x , y\right) | y = {x}^{2}\right\}$
This means that, taken any $x$, the point with coordinate $\left(x , {x}^{2}\right)$ is on the parabola. You are looking for the points $\left(x , y\right)$, where $y < {x}^{2}$. Since you know where the equality holds (i.e. on the parabola), you also know where the inequality holds: for any $x$, choose all the points with $y$ coordinates smaller than ${x}^{2}$.

We are doing nothing but describing with words the part of the plan below the graph, as shown -- so everything in the blue part (excluding the graph itself) is part of the solution.

graph{y< x^2 [-10.17, 9.83, -1.88, 8.12]}