Mathematics Education Program

EMAT 6680 Assignment 2

Try using the GC animation by replacing a, b, or c with an n and selecting an appropriate range for n.

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2. Fix two of the values for a, b, and c. Make at least 5 graphs on the same axes as you vary the third value. For example,

(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?

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.

iv. Generalize . . .

on the same axes. (i.e., use different values of a)

on the same axes using different values for d and f. Does varying d change the shape of the graph? the position? Does varying f change the shape or position of the graph?

Plot the points (d, f) on your graphs using

This is the GC 3.5 "2-vector" input and is essentially a parametric equation for a point.

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?

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.