2.1 transformations of parabolas

2.1 Transformations of Parabolas

10/12/2012

Graph is a parabola

VocabularyQuadratic Function :

a function that is written in the standard form: ax2 + bx + c where a ≠ 0

Vertex: The highest or lowest point of the parabola.

Vertex

Vertex

the line that divides a parabola into mirror images and passes through the vertex.

Axis of symmetry:

Axis of symmetry

Graph y = x2

Simplest quadratic equation

xxx

-2

-1

0

1

2

y

4

1

0

1

4

Graph y = -x2

xxx

-2

-1

0

1

2

y

-4

-1

0

-1

-4 Note: Graph is reflected in the x-axis.

Graph y = 2x2

xxx

-2

-1

0

1

2

y

8

2

0

2

8Note: Graph is stretched vertically by a factor of 2.

Graph y = x2

xxx

-2

-1

0

1

2

y

2

½

0

½

2Note: Graph shrinks vertically by factor of ½

Graph y = (x-2)2

xxx

0

1

2

3

4

y

4

1

0

1

4Note: Graph shifts 2 units to the right.

Graph y = (x+2)2

xxx

-4

-3

-2

-1

0

y

4

1

0

1

4Note: Graph shifts 2 units to the left.

Graph y = x2 - 2

xxx

-2

-1

0

1

2

y

2

-1

-2

-1

2Note: Graph shifts 2 units down.

Graph y = x2 + 2

xxx

-2

-1

0

1

2

y

6

3

2

3

6Note: Graph shifts 2 units up.

Graph y = (x-2)2 + 4

xxx

0

1

2

3

4

y

8

5

4

5

8Note: Graph shifts 2 units to the right and 4 units up.

Graph y = -½(x+2)2-2

Graph shrinks vertically by ½ and is reflected in

the x-axis

Graph shifts 2 units to the left.

Graph shifts 2 units down