# How do you graph the inequality #y>=(x-1)^2-3#?

##### 1 Answer

Please see below.

#### Explanation:

Let us first consider the graph of

This is the equation of a vertical parabola, which opens upwards, in vertex form and hence has a minima at

graph{(x-1)^2-3 [-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 origin

Hence in this area we have

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

hence this area satisfies

Now we are given the inequality

graph{y>=(x-1)^2-3 [-9.25, 10.75, -5.72, 4.28]}

Note that had we only