# How do you graph the inequality #y<=x^2+4x#?

##### 1 Answer

Please see below.

#### Explanation:

Let us first consider the graph of

and is the equation of a vertical parabola, which opens upwards and we have a minima at vertex

graph{x^2+4x [-9.25, 10.75, -5.72, 4.28]}

Observe that this divides the Cartesian plane in three parts of which one is the line graph of parabola,,

the other two parts are the area lying within the cup-shaped portion inside parabola. Observe that the point

Hence in this area we have

The third part is area outside the parabola and a point in this area is

hence this area satisfies

Now we are given the inequality

graph{y<=x^2+4x [-9.25, 10.75, -5.72, 4.28]}

Note that had we only