Question

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

Answer 1

`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

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

Explanation:

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]}