© Teachers Teaching with Technology (Scotland)
Teachers Teaching with Technology
T3 Scotland
Quadratic Graphs
©Teachers Teaching with Technology (Scotland)
QUADRATIC GRAPHS
Aim
The aim of this topic is to investigate quadratic functions of the form
y = (x + a)2 + b.
Objectives
Mathematical objectives
By the end of this topic you should know:
• how to describe and sketch a parabola by observation of its function.
• how to calculate the roots, maximum or minimum values of the function
• the transformation effects of varying the values of a and b.
Calculator objectives
By the end of this session you should:
• be able to graph functions via [Y=].
• be able todraw graphs of quadratic functions using appropriate settings, in different
graph types.
• be able to obtain table of values from the TI-83.
• be able to execute (run) a program stored on the TI-83.
STUDENT TASK
1.
Read the Calculator Skills Sheet (page 3) carefully before you start, this will ensure that
your TI-83 will function correctly.
2.
On the worksheets (page 4 -7), for each of the given equations you must:
i.
complete the table of values,
ii.
sketch the graph (use a different colour for each of the graphs on a page),
iii.
note whether the graph has a Maximum value or a Minimum value,
iv.
note what this value is
v.
note the value at which the graph intersects the y-axis.
3.
Using the information you have noted, complete the statements at the bottom of the
pages.
T3 Scotland
Quadratic Graphs
Page 1 of 7
QUADRATIC GRAPHS
Calculator skills sheet
Before we can start on this topic we must first ensure that your TI-83 is in the correct MODE
and that the STAT PLOTS are switched off, this ensures that the TI-83 and is going to operate
as we want it to.
1.
STAT
Press the 2
and PLOT buttons.
The display will look like this.
nd
Choose 4:PlotsOff and
ENTER
.
Now ENTER again.
The operation is DONE.
2.
MODE
Press the
button.
The display should look exactly like this.
If it does not look like this, then using the cursor keys highlight
ENTER
the correct item in each line and press
selection.
to change the
Notice: There can only be one item in each line highlighted.
3.
Now press the ZOOM and 6 .
This sets the window range to a built
in setting which will accommodate all
the work in this unit.
This screen is displayed
WINDOW
when
pressed.
4.
is
FORMAT
2 nd
Press the
and
.
This takes you to the WINDOW FORMAT screen.
It should look like this.
If it does not then using the cursor keys highlight the correct
item in each line and press
ENTER
.
Once the screen looks like this press
CLEAR
.
Notice: There can only be one item in each line highlighted.
T3 Scotland
Quadratic Graphs
Pag e 2 of 7
Function
Graph has a
Min or Max
Turning Point
Table of Values
1.
y = x2
x -3 -2 -1 0 1 2 3 4
y
2.
y = x2 + 7
x -3 -2 -1 0 1 2 3 4
y
3.
y = x2 - 5
x -3 -2 -1 0 1 2 3 4
y
4.
y = x2 + 10
x -3 -2 -1 0 1 2 3 4
y
5.
y = x2 - 3
x -3 -2 -1 0 1 2 3 4
y
Minimum or
Maximum
Value
Cuts the
Y-axis
at
How do I get a draw a graph on
the calculator ?
See Calculator Hint Sheet 2
y
x
Complete these statements
2
In equations of the form y = x + a
changing the value of a changes the ___________________________.
If a is positive then the parabola moves _____________________________.
If a is negative then the parabola moves _____________________________.
T3 Scotland
Quadratic Graphs
Pa
ge 3 of 7
Function
Graph has a
Min or Max
Turning Point
Table of Values
6.
y = -x2
x -3 -2 -1 0 1 2 3 4
y
7.
y = -x2 + 7
x -3 -2 -1 0 1 2 3 4
y
8.
y = -x2 - 5
x -3 -2 -1 0 1 2 3 4
y
9.
y = -x2 + 10
x -3 -2 -1 0 1 2 3 4
y
10.
y = -x2 - 4
x -3 -2 -1 0 1 2 3 4
y
Minimum or
Maximum
Value
Cuts the
Y-axis
at
y
x
Complete these statements
2
If a quadratic function has a positive x term then the graph has a __________ turning point.
2
If a quadratic function has a negative x term then the graph has a __________ turning point.
f(x) = x2 + C
T3 Scotland
y =_______.
intercepts the Y-axis at
Quadratic Graphs
Pa
ge 4 of 7
Function
Graph has a
Min or Max
Turning Point
Table of Values
11.
y = x2
x -3 -2 -1 0 1 2 3 4
y
12.
y = 2x2
x -3 -2 -1 0 1 2 3 4
y
13.
2
y = 4x
x -3 -2 -1 0 1 2 3 4
y
14.
y = ½x2
x -3 -2 -1 0 1 2 3 4
y
15.
y = -2x2
x -3 -2 -1 0 1 2 3 4
y
Minimum or
Maximum
Value
Cuts the
Y-axis
at
y
x
Make a conjecture about the
relationship between the graphs
.
of
y = x2
and
y = kx2
T3 Scotland
Quadratic Graphs
Pa
ge 5 of 7
Function
Graph has a
Min or Max
Turning Point
Table of Values
16.
y = x2
x -3 -2 -1 0 1 2 3 4
y
17.
y = (x + 4)2
x -3 -2 -1 0 1 2 3 4
y
18.
2
y = (x - 2)
x -3 -2 -1 0 1 2 3 4
y
19.
y = (x + 1)2
x -3 -2 -1 0 1 2 3 4
y
20.
y = (x - 3)2
x -3 -2 -1 0 1 2 3 4
y
Minimum or
Maximum
Value
Cuts the
Y-axis
at
y
x
Complete these statements
In quadratic functions of the form
y = (x + b)2
If b is positive then the graph is moved to the __________ by ______.
If b is negative then the graph is moved to the __________ by ______.
T3 Scotland
Quadratic Graphs
Pa
ge 6 of 7
In these examples you are given a table of values, you have to:
(1)
decide whether the function has a Max T.P or a Min.T.P, and what this value is
(2)
decide where the function cuts the Y-axis,
(3)
decide where the function cuts the X-axis,
(4)
find the function which would give this table of values.
How can you easily check your answers on the calculator?
Max / Min
Value
Table of Values
Cuts
Y-axis
Cuts
X-axis
Function
21.
x -3 -2 -1 0 1 2 3 4
y 12 7 4 3 4 7 12 19
y=
22.
x -4 -3 -2 -1 0 1 2 3
y 10 3 -2 -5 -6 -5 -2 3
y=
23.
x -4 -3 -2 -1 0 1 2 3
y 80 45 20 5 0 5 20 45
y=
24.
x -3 -2 -1 0 1 2 3 4
y 36 25 16 9 4 1 0 1
y=
25.
x -6 -5 -4 -3 -2 -1 0 1
y 1 0 1 4 9 16 25 36
y=
26.
x -6 -5 -4 -3 -2 -1 0 1
y 2 -1 -2 -1 2 7 14 23
y=
Now run the program MADQUAD.
This program will generate a quadratic of the form y = (x - a)2 - b.
You have look at the graph and identify the values of a and b.
The program will prompt you.
Good Luck
T3 Scotland
Quadratic Graphs
Pa
ge 7 of 7