Graphing Vertex Form Day 4

Graphing Vertex Form Day 4

Transformations

In this investigation you will graph different parabolas and compare them to what is known as the “basic parabola”.

The Basic Parabola

Table of Values

x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3

INVESTIGATION #1

x /
-3
-2
-1
0
1
2
3

What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3
x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3

What is the effect when a number is added or subtracted from the equation of the basic parabola?

INVESTIGATION #2

x /
-3
-2
-1
0
1
2
3

What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3
x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3

What is the effect when a number is added or subtracted to the x ( in brackets) from the equation of the basic parabola?

INVESTIGATION #3

x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3
x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3

What is the effect when a number (bigger that 1 or smaller than -1) is multiplied to the equation of the basic parabola?

INVESTIGATION #4

x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3
x /
-3
-2
-1
0
1
2
3
What is the vertex? / What is the direction of opening? / That is the “pattern”( how do you move from the vertex to the next point?) / Over 1
Over 2
Over 3

What is the effect when a number between -1 and 1 is multiplied to the equation of the basic parabola?

Summary:

Comparing to ,

1. means a vertical translation;if +k, move ___ k units

if -k, move __ k units

2. means a horizontal translation;if (x+h)2, move h units

If (x-h)2, move h units

3. means a vertical dilation;if a > 1, vertical ______by factor of a

if 0 < a < 1, vertical ____ by factor of

if a < -1, vertical______

if -1 < a <0, vertical______

Consider the following parabolas:

a)

Describe in words the transformations compared to .

State the following properties for each parabola and graph.

pattern

vertex

axis

direction of opening

min/max value

b)

Describe in words the transformations compared to .

State the following properties for each parabola and graph.

pattern

vertex

axis

direction of opening

min/max value

c)

Describe in words the transformations compared to .

State the following properties for each parabola and graph.

pattern

vertex

axis

direction of opening

min/max value