Let's put the inequality in slope-intercept form to make it easier to graph:

The inequality is now in slope-intercept form. Graph a line with slope  and y-intercept .

Because the inequality sign is greater than or equal to, a solid line should be used.

Next, test a point. The origin  is good choice. Determine if the following statement is true:

The statement is false. Therefore, the section of the graph that does not contain the origin should be shaded.

We can determine the lowest possible value of the expression by finding the -coordinate of the vertex of the parabola graphed from the equation . This is done by rewriting the equation in vertex form.

The vertex of the parabola  is the point .

The parabola is concave upward (its quadratic coefficient is positive), so  represents the minimum value of . This is our answer.

The equation of a parabola can be written in vertex form: .

The point  in this format is the vertex. If  is a postive number the vertex is a minimum, and if  is a negative number the vertex is a maximum.

In this example, . The positive value means the vertex is a minimum.

The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.

The graph below will be the answer, as it shows a parabolic curve.

From the vertex, we know that the equation of the parabola will take the form for some  .

To calculate that , we plug in the values from the other point we are given, , and solve for :

Now the equation is . This is not an answer choice, so we need to rewrite it in some way.

Expand the squared term:

Distribute the fraction through the parentheses:

Combine like terms:

Starting with

moves the parabola by  units to the right.

Similarly moves the parabola by  units to the left.

Hence the correct answer is option .

Start by visualizing the graph associated with the function :

Terms within the parentheses associated with the squared x-variable will shift the parabola horizontally, while terms outside of the parentheses will shift the parabola vertically. In the provided equation, 2 is located outside of the parentheses and is subtracted from the terms located within the parentheses; therefore, the parabola in the graph will shift down by 2 units. A simplified graph of  looks like this:

Remember that there is also a term within the parentheses. Within the parentheses, 1 is subtracted from the x-variable; thus, the parabola in the graph will shift to the right by 1 unit. As a result, the following graph matches the given function  :

This is an absolute value graph. Its equation takes the form , in which  represent the number of units that the base graph  is translated right and up respectively.

Since the graph of  is translated two units right and one unit down,  and , so the equation would be:

or 

To find the -intercept(s) of the graph, set  and solve for .

Rewrite this as the compound equation:

 or 

Solve each separately:

There are two -intercepts: