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]}