When we graph a hyperbola whose center is at the origin, we start by identifying if we have a vertical or horizontal hyperbola. We then plot the intercepts and graph the fundamental rectangle. Once this is completed, we can sketch the asymptotes. The graph of the hyperbola can then be sketched, each branch will go through the intercepts and approach the asymptotes.

Test Objectives
• Demonstrate the ability to identify the intercepts of a hyperbola centered at the origin
• Demonstrate the ability to sketch the asymptotes of a hyperbola
• Demonstrate the ability to sketch a vertical or horizontal hyperbola
Graphing Hyperbolas Practice Test:

#1:

Instructions: Graph each hyperbola.

a) $$y^2 - x^2 = 1$$

#2:

Instructions: Graph each hyperbola.

a) $$x^2 - \frac{y^2}{25} = 1$$

#3:

Instructions: Graph each hyperbola.

a) $$\frac{y^2}{16} - \frac{x^2}{16} = 1$$

#4:

Instructions: Graph each hyperbola.

a) $$x^2 - \frac{y^2}{9} = 1$$

#5:

Instructions: Graph each hyperbola.

a) $$\frac{y^2}{4} - x^2 = 1$$

Written Solutions:

#1:

Solutions:

a) $$y-intercepts: (0,1) , (0,-1)$$ $$Asymptotes:$$ $$y = x$$ $$y = -x$$ $$Fundamental\hspace{.25em}Rectangle:$$ $$(1,1),(-1,1),(-1,-1),(1,-1)$$

#2:

Solutions:

a) $$x-intercepts: (1,0) , (-1,0)$$ $$Asymptotes:$$ $$y = 5x$$ $$y = -5x$$ $$Fundamental\hspace{.25em}Rectangle:$$ $$(1,5),(-1,5),(-1,-5),(1,-5)$$

#3:

Solutions:

a) $$y-intercepts: (0,4) , (0,-4)$$ $$Asymptotes:$$ $$y = x$$ $$y = -x$$ $$Fundamental\hspace{.25em}Rectangle:$$ $$(4,4),(-4,4),(-4,-4),(4,-4)$$

#4:

Solutions:

a) $$x-intercepts: (1,0) , (-1,0)$$ $$Asymptotes:$$ $$y = 3x$$ $$y = -3x$$ $$Fundamental\hspace{.25em}Rectangle:$$ $$(1,3),(-1,3),(-1,-3),(1,-3)$$

#5:

Solutions:

a) $$y-intercepts: (0,2) , (0,-2)$$ $$Asymptotes:$$ $$y = 2x$$ $$y = -2x$$ $$Fundamental\hspace{.25em}Rectangle:$$ $$(1,2),(-1,2),(-1,-2),(1,-2)$$