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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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Presentation Transcript
slide2

What is

the hang

time of a

football?

slide4

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

slide5

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.

slide8

Gallileo was the first to show that the path

of an object thrown in space is a parabola.

graphing a parabola1
Graphing A Parabola

y = x2 – 2x – 3

graphing a parabola2
Graphing A Parabola

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

parabola characteristics
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
slide15

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

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

a = -1 b = 4 c = -1

Vertex is at

slide16

Vertex?

Max or Min?

Axis of Symmetry?

slide17

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

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

a = 1 b = -2 c = - 8

Vertex is at

slide18

Vertex?

Max or Min?

Axis of Symmetry?

homework
Homework

Graphing Parabolas Homework #1

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