Student Page 4.2.3 Multiplying Lines Electronically With Desmos
Now that you have graphed the product of two lines by hand, explore the product of two lines using Desmos as you complete the student page, Multiplying Lines Electronically With Desmos. Do you get the same results? What more do you notice?
1.
Set up Desmos to play with products of linear functions, as follows:
(a)
Type
(b)
Type
(c)
Type
(d)
Type
2.
Play with the
(a)
How does the graph of the product of two lines change as you change
(b)
Why does the change in
(c)
What happens to the product graph with
(d)
From your previous mathematical experiences, what is the graph of the product called?
3.
Play with the
4.
Edit the first input line to be
(a)
For what values of
(b)
For Task 4.2.3.4.a, is the parabola wider than
(c)
For what values of
(d)
Explain what
5.
Turn off
6.
Continute to play with all three sliders,
(a)
Try each of these three possibilities:
(i)
Both lines have positive slopes.
(ii)
Both lines have negative slopes. (What additional change do you need to make?)
(iii)
One line has a positive slope and the other line has a negative slope.
(b)
How can you tell from the lines what a parabola created from the product of the lines will open upward? Reason from the equations of the lines and the parabola.
(c)
How can you tell from the lines what a parabola created from the product of the lines will open downward? Reason from the equations of the lines and the parabola.
(d)
How can you tell from the lines where the parabola will intersect the
(e)
How can you tell from the lines where the parabola will intersect the
(f)
What is a line of symmetry?
(g)
How can you find the line of symmetry for a function that is the product of two lines? Why does this make sense?
(h)
Each parabola has a highest or lowest point, called the vertex. What information about the vertex can you determine from the lines? Explain.