Height (ft)
Distance (feet)
Chapter 9
Section 1 and 2
Quadratic Function
A quadratic function is of the form
y = ax2 + bx + c where a≠0.
The graph of a quadratic function is called
a parabola.
Different Forms of
Quadratic Equations
y = a (x – h)2 + k
Standard Form: y = ax2 + bx + c
Intercept Form: y = a(x – p) (x – q)
Vertex Form:
We will explore each of these
forms in this section.
Each form yields different
information that can be used to
graph the equation.
Let’s first look at the graph of a
quadratic equation.
For the helicopter to fly above the rainbow parabola, how
high must the copter fly? (In other words what is the
maximum value of the parabola)
Below is a picture of a rainbow that makes a perfect
parabola.
- What is the vertex of the parabola?
Trajectories (Projectile Motion): Everything on the planet Earth is
subject to gravity. When on object is thrown or forced in a direction not
on the ground, eventually gravity grabs it and drags it down. The path the
Boy!
I love
object follows it that
of aDo
Parabola.
Physics 
Galileo discovered that falling objects follow a parabolic path which we
now call projectile motion.
Older Spacecraft: Many of the older space missions followed a
parabolic path. When launched, the spacecraft never directly went
into the atmosphere... that would surely cause it to burn up. Rather, it
entered at an angle. While in space, it would continue to fall to the
Earth and eventually, could be recovered.
Parabolas are used in war.
Yes, parabolas can be complicated like the previous
examples. But, we see parabolas everyday!!
Can you think of any other examples?
Definition
Is the vertex always the maximum value of
the parabola?
The highest or lowest point on the graph of
a quadratic function is called the vertex.
Maximum Value of a Parabola
In the parabola on the
left, the maximum
value is the point
(2,1).
Identify the vertex.
This is the graph
y=
2
x
What is the vertex?
Minimum Value
Identify the vertex.
This is the graph
y = -x2
What is the vertex of y= -x2?
Maximum Value
Symmetry
Parabolas also have the special quality
of being symmetric.
What is symmetry?
When have we seen symmetry in
Algebra 2 before?
Let’s practice
drawing lines
of symmetry!
St. Peter's Basilica
Rome, Italy
Practice identifying the vertex and
line of symmetry of each parabola.
Line of Symmetry?
Vertex?
Line of Symmetry?
Vertex?
Line of Symmetry?
Vertex?
Where have we seen
parabolas before?
The Gateway Arch in St. Louis, MO uses an upside down parabola to create a
sense of a "gateway" or door to the west
National Mall,
Washington, D.C.
Parabolas across the
Potomac River, Washington, D.C.
The Skycoaster in
Lagoon- Farmington,
UT
Don’t Worry!
Graphing Parabolas
is less scary than
riding parabolas!!
The Golden Gate Bridge
is a Suspension Bridge
that uses parabolas
Get into assigned groups. These are your task groups.
Get into your task groups and complete the assignment
given (a, h, or k).
Work together with your groups to compile the different
concepts you explored in your task groups.
Write your observations on a post-it poster.
Roles are assigned to each person in your group:
 Observation Recorder (records observations from the group)
 Poster Creator (creates poster with collaborative effort from
group)
 Presenter (will present the findings of the group)
 Task Officer (make sure everyone stays on task)
 Supplier (Make sure supplies are put away, workspace is clean,