Collectively the methods were going to be looking at

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Unformatted text preview: e vertices. These are ( 8, -1) and ( -2, -1) . Next we should get the slopes of the asymptotes. These are always the square root of the number under the y term divided by the square root of the number under the x term and there will always be a positive and a negative slope. The slopes are then ± 7 . 5 Now that we’ve got the center and the slopes of the asymptotes we can get the equations for the asymptotes. They are, © 2007 Paul Dawkins 221 College Algebra y = -1 + 7 ( x - 3) 5 y = -1 - and 7 ( x - 3) 5 We can now start the sketching. We start by sketching the asymptotes and the vertices. Once these are done we know what the basic shape should look like so we sketch it in making sure that as x gets large we move in closer and closer to the asymptotes. Here is the sketch for this hyperbola. [Return to Problems] (b) In this case the hyperbola will open up and down since the x term has the minus sign. Now, the center of this hyperbola is ( -2,0 ) . Remember that sinc...
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