DRESSING UP Y = X2
Introduction: This investigation examines the effects of three types of transformations of the basic quadratic function
.
· The first transformation is multiplying by a number.
Some examples are: , , .
· The second transformation is adding or subtracting a constant to the variable .
Some examples are: and .
· The third transformation is adding or subtracting a constant to the term.
Some examples are: and .
We will then examine the combined effects of all three transformations together. Some examples are:
and . In general, we will investigate the effects of a, h and k on the
quadratic function .
Part A: Knowing the basic function .
Complete the following table for . These points will be the key points you will use all the time. Sketch the graph
of the function on the grid below.
x y
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9
, 1. What is the shape of the graph called?
parabola
2. What are the coordinates of the vertex? State the domain and range.
(0,0)
3. What is the equation of the axis of symmetry? X=0
4. State the values of the parameters a, h,and k. 1,0,0
Use a graphing technology to do the following investigations.
Part B: The effects of a on . Graph in on your calculator and on the grid . This is the basic
parabola, compare all the rest to this one.
1. On the same set of axes sketch the graph of where
a = 0.25, 0.5, 2, 5, -0.5, -1, -2. Sketch the graphs on the grid
and label each graph with its equation. Using a different colour
for each graph would be good.
The sketches should be quite clear from your graphing calculator!
2. a. Does changing a change the position of the vertex?
no
b. In general, what effect does a have on the graph?
a stretches the graph vertically!
c. As the size of | a | increases, what happens to the graph?
It becomes stretched vertically more
d. When a is positive, which way does the parabola open?
Introduction: This investigation examines the effects of three types of transformations of the basic quadratic function
.
· The first transformation is multiplying by a number.
Some examples are: , , .
· The second transformation is adding or subtracting a constant to the variable .
Some examples are: and .
· The third transformation is adding or subtracting a constant to the term.
Some examples are: and .
We will then examine the combined effects of all three transformations together. Some examples are:
and . In general, we will investigate the effects of a, h and k on the
quadratic function .
Part A: Knowing the basic function .
Complete the following table for . These points will be the key points you will use all the time. Sketch the graph
of the function on the grid below.
x y
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9
, 1. What is the shape of the graph called?
parabola
2. What are the coordinates of the vertex? State the domain and range.
(0,0)
3. What is the equation of the axis of symmetry? X=0
4. State the values of the parameters a, h,and k. 1,0,0
Use a graphing technology to do the following investigations.
Part B: The effects of a on . Graph in on your calculator and on the grid . This is the basic
parabola, compare all the rest to this one.
1. On the same set of axes sketch the graph of where
a = 0.25, 0.5, 2, 5, -0.5, -1, -2. Sketch the graphs on the grid
and label each graph with its equation. Using a different colour
for each graph would be good.
The sketches should be quite clear from your graphing calculator!
2. a. Does changing a change the position of the vertex?
no
b. In general, what effect does a have on the graph?
a stretches the graph vertically!
c. As the size of | a | increases, what happens to the graph?
It becomes stretched vertically more
d. When a is positive, which way does the parabola open?
