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Exercise 1:
Are you faster than a speeding bullet? Able to
leap tall buildings in a single bound? Able to graph any line in less than 30 seconds?
We'll give you a break on the first two, but, for the last one, you should be an old pro.
You can assess your line graphing abilities and brush up, if necessary, at Equations of Lines -- A
Tutorial from Washington State University. Take the entry test and, if you don't do
very well, run through the problems for some practice. |
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Exercise 2:
Now that you are an expert at graphing lines,
let's investigate solving system of equations by graphing. Go to the Intersecting Lines
Applet from Washington State University. This site will allow you to move two lines
around (by dragging the squares) and change their slopes (by dragging the circles). Be
sure to maximize your browser screen so that you can see the top four lines of information
at the right of the graph. |
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Exercise 3:
Go to the Quadratic Equation Root Calculator.
Enter in values of a = 5 and b = 5. Find the values of c that give two real roots and the
values that give two imaginary roots. Use the discriminant to prove your results. Now do
the same with a = 1 and b = 5 and then with a = 1 and b = -5. |
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Exercise 4:
To see the graphical side of what is happening
in Exercise 3, go to the Equation Grapher.
Graph the parabolas with the given values of a and b and the various values of c that you
tried. What can you conclude about the effect of the constant, c, on the graph and the
types of roots?
(answer) |
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Exercise 5:
In section 1.5, you learned about complex
numbers. One of the most fascinating applications of these numbers is fractals. To learn
about what fractals are, go to Fabio Cesari's Fractal Explorer. Read the first
page and the following sections: About complex numbers, Mandelbrot set, Julia sets. Then
take his Guided Tours 1 and 2. The tours will take a few minutes to load, but they are
well worth the wait. |
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Exercise 6:
Now that you've learned what fractals are,
it's time for you to create your own! Go to the following sites and create a fractal at
each: The Fractal Microscope, The Fractory. Be creative and be sure to
play with the settings on the sites. The trick will be saving them properly so you can
turn them in to your instructor. PC-Users: To save, right-click *on the image* and
choose 'Save Image As...'
Mac-Users: To save, click and hold *on
the image* and choose 'Save Image
As...' |
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