How do you graph y<x^2?

1 Answer

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
{(x,y) | y=x^2}
This means that, taken any x, the point with coordinate (x,x^2) is on the parabola. You are looking for the points (x,y), 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]}