Analyzing Polynomial Functions

1
Analyzing Polynomial Functions

• Objectives 2i and 2k

2
OBJECTIVES

• 2i Determine the solutions to quadratic equations
  by using graphing, tables, completing the square,
  the quadratic formula, and to include real-life
  applications. (DOK 1)
• 2k Graph and analyze quadratic functions to
  include relating x intercepts to solutions and
  real-life applications.

3
Kangaroo Jump

• The height of a kangaroo can be modeled by the
  quadratic function
• h(t) -16t2 24t
• where h is the height in feet the kangaroo jumps
  at a given time t in seconds.
• What is the dependent variable?
• What is the independent variable?

4
h(t) -16t2 24t

• What are the x-intercepts and what information do
  they provide?
• What is the y-intercept and what information does
  it provide?
• What is the vertex and what information does it
  provide?
• What is the range of the function?
• What is the domain of the function ?

5
Projectiles

• A projectile is fired vertically upward from a
  point above the ground, modeled by the function
  h(t) -16t2 76t 20, where t is measured in
  seconds and h is measured in feet.

6
h(t) -16t2 803t 600

• What is the x-intercept and what information does
  it provide?
• What is the y-intercept and what information does
  it provide?
• What is the vertex and what information does it
  provide?
• Domain Range ?

7
Population Growth

• The population growth of a certain species of
  bacteria can be modeled by a quadratic function,
• P(t) 0.5t2 -7t 50
• where t the time measured in minutes and p is
  the population measured in hundreds.
• During the first few minutes of observation, the
  population decreases, but then begins to increase
  again over time.
• Interpret what the ordered pair (2, 38) means for
  this model.

8
P(t) 0.5t2 -7t 50

• What is the x-intercept and what information does
  it provide?
• What is the y-intercept and what information does
  it provide?
• What is the vertex and what information does it
  provide?
• If the bacteria growth was observed for 20
  minutes, what was the initial population and what
  was the ending population?
• Domain Range and what do they mean ?

9
Application Poster Lab

• Ms.Coon