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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 2.5,
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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