Exponential Translations Use this Desmos page to compare the translations of exponential equations with something you know from Unit 2: translations of the vertex form of quadratic equations.
Remember the vertex is the point (h 1, 1) and the parent form is = 2. For exponential the key point that you should focus on is (0,1) and note how it shifts from its parent form = (we will use b=2 for most of these).
For the following questions start with a=1, h=0, and k=0 for both equations.
1. Move the slider for k for both equations. Describe how the functions shift (table
rows 1-2)
2. Return k=0 for both equations. Move the slider for h for both and describe how
the functions shift (table rows 3-4)
3. Set h and k to 0. Move the sliders for a. What happens when a is negative (table
row 5)?
4. What happens when |0 < < 1|or is a fraction/decimal less than 1 (table row
6)?
5. What happens when > 1or is getting larger? (table row 6)?
6. What happens when <− 1or is getting smaller? (table row 7)?
Exponential Only
7. Set a=1, h=0, and k=0 for the exponential and move the slider for b. What happens as b increases (table row 8)? Also notice what happens to the point (0,1)
8. What happens as b decreases (table row 9)?
9. Something strange happens when b=1. What happens and explain why (table
row 10)?
10.What happens when 0 < < 1or in other words is a fraction/decimal less than 1
(table row 11)?
11. What would be the equation of a function, () that shifted () = 2 to the left by 4 and up by 3? () =_
Name:_
Action
Quadratic
Exponential
1
As k increases or is positive
2
As k decreases or is negative
3
As h increases or is positive
4
As h decreases or is negative

5
When a is negative
6
As a increases
7
As a decreases
8
As b increases
skip
9
As b decreases
skip
10
When b=1
skip
11
When 0 < < 1
skip
If you get stuck on any of these check out this t