How long does a firework stay in the air?

What is the hangtime of afootball?

How does a satellite dish work?

Chapter 10 Quadratic Functions

Quadratic Functions are used to simulate real-life situations. A quadratic function is an equation in the form:

y = ax2 + bx + c

10-1 Graphing Quadratic Functions

Objectives:

I will be able to graph a quadratic function.

I will be able to find the equation of the axis of symmetry and the coordinates of the vertex.

                                                                                                                                                                       

The graph of a quadratic function is called a parabola. It looks like a U or an upside down U.

4

2

-2

-4

-5 5

f x = x2-2x-34

2

-2

-4

-5 5

f x = -x2-2x +3

Gallileo was the first to show that the path of an object thrown in space is a parabola.

Graphing A Parabola

x y = x2 – 2x – 3 y

-2

-1

0

1

2

3

4

To graph a parabola we create a table of values and then plot the points. Lets Graph: y = x2 – 2x – 3

Graphing A Parabolay = x2 – 2x – 3

x y

-2 5

-1 0

0 -3

1 -4

2 -3

3 0

4 5

Graphing A ParabolaLets Graph: y = -x2 + 2x + 1

x y = -x2 + 2x + 1 y

-1

0

1

2

3

y = -x2 + 2x +1

x y

-1 -2

0 1

1 2

2 1

3 -2

Graph It!

Parabola CharacteristicsQuadratic Equation: y = ax2 + bx + c

– The maximum or minimum point is called the vertex.

– If a is positive the graph opens up. (Minimum)– If a is negative the graph opens down.(Maximum)– The line that divides a parabola directly in half is

called its axis of symmetry.– The axis of symmetry and vertex (turning point)

can be found using the equation

a

bx

2

Golden Gate Bridge

The cables that act as suspension are parabolas.

Lets look at the equation: y = -x2 + 4x – 1

a = -1 b = 4 c = -1

Vertex is at a

bx

2

y = -x2 + 4x – 1

x y

The general parabola equation is: y = ax2 + bx + c

)1(2

)4(

2

4

2

y = -x2 + 4x – 1

x y

0 -1

1 2

2 3

3 2

4 -1

Vertex?

Max or Min?

Axis of Symmetry?

Lets look at the equation: y = x2 – 2x – 8

a = 1 b = -2 c = - 8

Vertex is at a

bx

2

y = x2 – 2x – 8

x y

The general parabola equation is: y = ax2 + bx + c

)1(2

)2(

2

2 1

y = x2 – 2x – 8

x y

- 1 - 5

0 - 8

1 - 9

2 - 8

3 - 5

Vertex?

Max or Min?

Axis of Symmetry?

Homework

Graphing Parabolas Homework #1