# Translations, Shrinks, and Stretches

- Author:
- Sheri Stayton

- Topic:
- Parabola, Sine, Translation

The following helps students see how changing parameters affects horizontal and vertical translations as well as horizontal and vertical stretches and shrinks analogously in parabolic, absolute value, logarithmic, and sinusoidal functions using sliders.

1. Begin with slider D. Move the slider and pay attention to how the graphs change as well as how the equations in the algebra view change. In your own words, explain how the equation is changing and how that change affects the graphs.
2. Next, move slider C. Move the slider and pay attention to how the graphs change as well as how the equations in the algebra view change. In your own words, explain how the equation is changing and how that change affects the graphs.
3. Were you surprised about the effect slider C had on the graphs? If so, explain how the movement of the graphs were different than you expected.
4. Next, move slider A. Move the slider and pay attention to how the graphs change as well as how the equations in the algebra view change. In your own words, explain how the equation is changing and how that change affects the graphs.
5. Next, move slider B. Move the slider and pay attention to how the graphs change as well as how the equations in the algebra view change. In your own words, explain how the equation is changing and how that change affects the graphs.
6. Were you surprised about the effect slider B had on the graphs? If so, explain how the movement of the graphs were different than you expected.
7. Reread your responses to questions 3 and 6. Do you see a relationship between the general behavior of these two parameters? Elaborate.
8. If a peer told you that the parameters A and D behaved exactly as they expected but that parameters B and C behaved the opposite of what they expected, how would you help them make sense of this?