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

Mar 17, 2016

$y = {x}^{2}$ is the parabola with vertex at the origin and axis along x = 0, $y \ge 0$, The entire plane beneath this parabola is the graph of $y < {x}^{2}$.

Mar 17, 2016

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 $\left(3 , 2\right)$ 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 $\left(- 1 , 6\right)$ 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]}