Graphing Quadratic Functions

A quadratic function is an equation of the form:

y = ax2 + bx + c

How long does a firework stay in the air?

What is the hangtime of afootball?

How does a satellite dish work?

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

y = 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

-2

-1

0

1

2

3

4

y = -x2 + 2x +1

x y

-2 -7

-1 -2

0 1

1 2

2 1

3 -2

4 -7

y = -x2 + 2x + 1

Vertex (Turning Point)

Quadratic Equation: y = ax2 + bx + c

The maximum or minimum point is called the vertex or turning point of the parabola.

If a is positive the graph looks like a smile. (Minimum)

If a is negative the graph looks like a frown. (Maximum)

Axis of Symmetry

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.

3) y = -x2 + 4x – 1

Vertex is at:a

bx

2

y = -x2 + 4x – 1

x y

y = ax2 + bx + c

y = -x2 + 4x – 1

x y

-1 -6

0 -1

1 2

2 3

3 2

4 -1

5 -6

Vertex?

Max or Min?

Axis of Symmetry?

4) y = x2 – 2x – 8

Vertex is at:a

bx

2

y = x2 – 2x – 8

x y

y = ax2 + bx + c

y = x2 – 2x – 8

x y

-2 0

-1 -5

0 -8

1 -9

2 -8

3 -5

4 0

Vertex?

Max or Min?

Axis of Symmetry?

Homework

Graphing Parabolas Homework #1