1. Section 9.6 Day 1 Analyzing Functions with Successive Differences
Algebra 1

2. Linear Equations - Graph

3. Linear Equations - Equation
General Equation:
𝑦=𝑚𝑥+𝑏
Example:
𝑦=8𝑥−9

4. Linear Equations – Ordered Pairs
The slope between all ordered pairs should be the same Example: { 2, 7 , 1, −1 , 0, −9 , 4, 23 } Slope between all points is 8

5. Linear Equations - Table
The y-values increase or decrease by the same number (first differences)
Example:
Notice that each y-value decreases by 2 X -1 1 2 Y -3 -5 -7

6. Quadratic Equations - Graph

7. Quadratic Equations - Equation
Standard Form: 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐
Vertex Form: 𝑦=𝑎 𝑥−ℎ 2 +𝑘
Intercept Form: 𝑦=(𝑥−𝑝)(𝑥−𝑞)

8. Quadratic Equations – Ordered Pairs
When you graph the points, they should represent a parabola shape
Example: { −3, 10 , −1, 2 , 2, 5 , 4, 17 }

9. Quadratic Equations - Table
The y-values increase or decrease by the same number for second differences
Example:
The first differences change by different numbers. However, the second differences increases by 2 X -1 1 2 Y -2

10. Exponential Equations - Graph

11. Exponential Equations - Equation
Exponential Growth:
𝑦=𝑎 𝑏 𝑥 when 𝑏>1, 𝑎>0
Exponential Decay:
𝑦=𝑎 𝑏 𝑥 when 0<𝑏<1, 𝑎>0

12. Exponential Equations – Ordered Pairs
When you graph the points, it should look like an exponential graph
Example: { −3, 125 , −1, 5 , 1, 1 5 , 4, }

13. Exponential Equations - Table
The ratios between the y-values is a consistent number
Example:
Notice that the ratio between the y-values is 4 X -1 1 2 Y
1/4 4 16

14. Activity Cut out the flash cards
Group the cards into the following categories
Linear
Quadratic
Exponential
Neither/None of the above categories