The Department of Mathematics Education
3. Adjust the ranges on the
axes in Problem 2 to produce graphs that can be read, interpreted,
and used for demonstration.
4. Interpret your graphs. What happens to
(i.e., the case where b=1 and c=2) as a
is varied? Is there a common point to all graphs? What is it?
What is the significance of the graph where a = 0? Do similar
interpretations for other sets of graphs. How does the shape change?
How does the position change?
5. For demonstration, is it better to graph 5 graphs at once or
produce them in sequence adding one at a time? What are the pedagogical
implications of this observation?
6. Graph the parabola
i. Overlay a new graph replacing each x by
(x - 4).
ii. Change the equation to move the vertex of the graph into
the second quadrant.
iii. Change the equation to produce a graph concave down that
shares the same vertex.
7. Try several graphs of
on the same axes. (i.e., use different values
of a)
8. Produce several ( 5 to 10) graphs of
on the same axes using different values for
d. Does varying d change the shape of the graph?
the position?
9. Graph
Now, on the same axes graph
Describe the new graph. Change the range on
the y-axis from -25 to 25 and redraw. Now interpret. What do you
think will happen if we change the coefficients of the xy term?
Systematically try different coefficients for the xy term. Are
they always the same types of curves?
What about coefficients which are close to zero?
How does the sign of the coefficient change the graph?
10. Graph
Now, on the same axes, graph
Describe the new graph. Try different coeffcients
for the xy term. What kinds of graphs do you generate? What coefficients
mark the boundaries between the different types of graphs? How
do we know these are the boundaries? Describe what happens to
the graph when the coefficient of the xy term is close to the
boundaries.
Did your find this?
Or,what about this?
Or, try this one.
Return
to EMAT 6680 Home Page
