Transcript Solving Quadratic Equation by Graphing

Analyzing Polynomial Functions
Objectives 2i and 2k
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.
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?
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 ?
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.
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 ?
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.
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 ?
Application Poster Lab
 ***Ms.Coon