How do you graph the inequality #y < x^2#?

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Answer 1 · 2016-03-17T11:40:45

#y = x^2# is the parabola with vertex at the origin and axis along x = 0, #y >= 0#, The entire plane beneath this parabola is the graph of #y < x^2#.

Answer 2 · 2016-03-17T11:49:20

Portion of the plane below the curve #y=x^2#, not including the curve #y=x^2#.

To draw the graph of inequality #y<x^2#, first draw the graph of #y=x^2#, which will appear as shown below.

The graph divides the plane in three parts,

(a) the line #y=x^2#, itself

(b) the portion of the plane below the line.Consider a point #(3,2)# in this for which #y<x^2# (as #2<3^2#). Hence, in this area #y<x^2#.

(c) the portion of the plane above the line.Consider a point #(-1,6)# in this for which #y>x^2# (as #6>(-1)^2)#. Hence, in this area #y>x^2#.

Hence, (b) is the solution of inequality #y<x^2# and solution does not include the curve #y=x^2#.

graph{y=x^2 [-4, 4, -5, 5]}