Find the standard form of the hyperbola.

Subtract from both sides of the equation.

Divide each term by to make the right side equal to one.

Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .

This is the form of a hyperbola. Use this form to determine the values used to find the asymptotes of the hyperbola.

Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .

The asymptotes follow the form because this hyperbola opens left and right.

Simplify .

Add and .

Multiply by .

Simplify .

Add and .

Rewrite as .

This hyperbola has two asymptotes.

The asymptotes are and .

Asymptotes:

Asymptotes:

Remove parentheses.

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is , where is the slope and is the y-intercept.

Find the values of and using the form .

The slope of the line is the value of , and the y-intercept is the value of .

Slope:

y-intercept:

Slope:

y-intercept:

Any line can be graphed using two points. Select two values, and plug them into the equation to find the corresponding values.

Find the x-intercept.

To find the x-intercept(s), substitute in for and solve for .

Solve the equation.

Rewrite the equation as .

Add to both sides of the equation.

x-intercept(s) in point form.

x-intercept(s):

x-intercept(s):

Find the y-intercept.

To find the y-intercept(s), substitute in for and solve for .

Solve the equation.

Remove parentheses.

Remove parentheses.

Subtract from .

y-intercept(s) in point form.

y-intercept(s):

y-intercept(s):

Create a table of the and values.

Graph the line using the slope and the y-intercept, or the points.

Slope:

y-intercept:

Slope:

y-intercept:

Plot each graph on the same coordinate system.

Graph f(x)=int (x-2)