GUIDED NOTES – Lesson 2-3
Average Rate of Change
Name: ______________________ Period: ___
Objective: I will find the rate of change of a quadratic function. I can write and solve application problems using
quadratic functions.
The AVERAGE RATE OF CHANGE between two points (where x1 = a and x2 = b) in a function f(x) is defined by the
following formula:
f ( x) f  b   f  a 

x
ba
This is equal to the SLOPE of the _______________________, which is a line
directly connecting two points on the function.
EXAMPLE: What is the average rate of change between the two points shown
on this quadratic function?
EXAMPLE: Determine the rate of change on the given intervals, using the graph of the
function.
a)
Find the rate of change for x = 1 to x = 2
b)
Find the rate of change for x = 0 to x = 2
c)
Find the rate of change for x = 3 to x = 5
d)
Find the rate of change for x = 0 to x = 6
EXAMPLE: Given the function: f(x) = x2 + x – 6
a)
Find the rate of change for x = 1 to x = 2
b) Find the rate of change for x = 0 to x = 3
c) Which is the greater rate of change?
APPLICATIONS OF QUADRATICS - Quadratic functions have many practical uses.
One is that they can be used to model projectiles, objects being _____________, _____________ or ____________.
The vertical motion problems talk about an object falling to earth.
Formula for FEET
Formula for METERS
h(t) = height at time t
h(t )  16t 2  ho
h(t )  4.9t 2  h0
v=
h(t )  16t 2  vt  ho
h(t )  4.9t 2  vt  h0
h0 =
EXAMPLE: A ball is thrown vertically upward with an initial velocity of 48 feet per
second with an initial height of 8 feet off the ground.
a) Write a function that models this scenario.
b) What is the maximum height of the ball?
c) When did this occur?
d) State the domain and range for the function
EXAMPLE: Imagine that a penny is dropped from the observation deck of the Empire
State Building, which is 381 meters above ground level. (do not drop objects from
buildings in real life)
a) Write a function that models this scenario.
b) What is the maximum height of the penny?
c) What is the height of the penny after 2 seconds?
d) How long will it take for the penny to hit the ground?
e) State the domain and range for the function.