AP Precalculus / Unit 1: Polynomial and Rational Functions
1.3 Rates of Change in Linear and Quadratic Functions
Notes
- Linear: the average rate of change is constant over every interval.
- Quadratic: the average rates over equal-length consecutive intervals change at a constant rate (constant second differences).
Practice
Outputs at $x=0,1,2,3$ are $2, 5, 8, 11$. The function is:
Constant differences of 3.
Outputs at $x=0,1,2,3$ are $1, 2, 5, 10$. First differences are 1, 3, 5, so the function is:
Second differences are a constant 2.
For a concave-up quadratic, average rates of change over consecutive equal intervals:
Concave up means rates increase.
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