Height (ft)

Distance (feet)

Chapter 9Section 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

Vertex Form: y = a (x – h)2 + k

Standard Form: y = ax2 + bx + c

Intercept Form: y = a(x – p) (x – q)

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 object follows it that of a Parabola.

Galileo discovered that falling objects follow a parabolic path which we now call projectile motion.

Boy! Do I love Physics

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

The highest or lowest point on the graph of a quadratic function is called the vertex.

Is the vertex always the maximum value of the parabola?

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 = x2

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

How ironic!?

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

Exploring Parabolas: Vertex Form

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,

and the desks are put back when instructed)