# How long does a firework stay in the air? - PowerPoint PPT Presentation

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How long does a firework stay in the air?. What is the hang time of a football?. 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 = ax 2 + bx + c.

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How long does a firework stay in the air?

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#### Presentation Transcript

How long does a firework

stay in the air?

What is

the hang

time of a

football?

### How does a satellite dish work?

Quadratic Functions are used to simulate real-life situations.

A quadratic function is an equation in the form:

y = ax2 + bx + c

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.

Gallileo was the first to show that the path

of an object thrown in space is a parabola.

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

### Graphing A Parabola

Lets Graph: y = -x2 + 2x + 1

Graph It!

### Parabola Characteristics

Quadratic 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

The cables that act as suspension are parabolas.

Golden Gate Bridge

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

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

a = -1b = 4c = -1

Vertex is at

Vertex?

Max or Min?

Axis of Symmetry?

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

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

a = 1b = -2c = - 8

Vertex is at

Vertex?

Max or Min?

Axis of Symmetry?

### Homework

Graphing Parabolas Homework #1