|
This page contains
a Lab Investigation worksheet for discovering (or reinforcing) information
about parabolas. A .pdf worksheet page is available for use in your
classroom. A teacher comment/answer sheet appears at the bottom of the
page.
(Directions are applicable to the TI-82, TI-83, TI-83+
and TI-84+
graphing calculators.)
Download a worksheet
for use in your classroom.
Investigating
Parabolas.pdf
Lab Sheet-Investigating
Parabolas (here is a glimpse of what is on the worksheet)
Graph the following
equations using the graphing calculator.
Use the STANDARD window (ZOOM
6). Sketch your graphs.
Answer the question associated with each problem.
1. Y1=
x2
Y2= x2 + 2
Y3= x2 + 4
What happens to the graph when
a number is added to x2?
_________________________
_________________________
_________________________ |
|
2. Y1=
x2
Y2= x2 - 5
Y3= x2 - 2.5
What happens to the graph when
a number is subtracted from x2?
_________________________
_________________________
_________________________ |
|
3. Y1=
x2
Y2= 2x2
Y3= 6x2
What happens to the graph when
x2
is multiplied by a number greater than 1?
_________________________
_________________________
_________________________
_________________________
|
|
4. Y1=
x2
Y2= 0.5x2
Y3= 0.2x2
What happens to the graph when
x2
is multiplied by a number between 0 and 1?
_________________________
_________________________
_________________________
_________________________ |
|
5.
Y1= x2
Y2= -x2
Y3= -2x2
(be careful to use the negation key and not the subtraction key)
What happens to the graph when the
coefficient of x2 is negative?
_________________________
_________________________
_________________________ |
|
6. Y1= 2x2
+ 3
Y2= -2x2 + 3
Compare these two graphs.
What observations can be made?
__________________________
__________________________
__________________________
__________________________ |
|
7. Y1=
0.5x2
-2
Y2= -0.5x2 + 2
Compare these two graphs.
What observations can be made?
_________________________
_________________________
_________________________
_________________________ |
|
Teacher
Answer Sheet
| |
Graph |
Possible
Student Answers |
| 1. |
 |
What happens to the graph when
a number is added to x2?
The graph is
shifted vertically upward. Since these were positive values, the
graph moved up. |
| 2. |
 |
What happens to the graph when
a number is subtracted from x2? The
graph is shifted vertically downward. Since these were negative
values, the graph moved down. |
| 3. |
 |
What happens to the graph when
x2
is multiplied by a number greater than 1?
The span
("width") of the graph is becoming more narrow. The graph is
becoming steeper at a faster rate. |
| 4. |
 |
What happens to the graph when
x2
is multiplied by a number between 0 and 1?
The span
("width") of the graph is becoming wider. The graph is
becoming steeper at a slower rate. |
| 5. |
 |
What happens to the graph when the
coefficient of x2 is negative?
The graph opens
downward. |
| 6. |
 |
Compare these two graphs.
What observations can be made?
The shift of +3
moved both graphs vertically up 3 units. The negative coefficient
makes the graph open downward. (The graphs are reflections of one another
over y = 3.) |
| 7. |
 |
Compare these two graphs.
What observations can be made?
The +2 shifted
the graph vertically up two units and the -2 shifted the graph vertically
down two units. The negative coefficient makes the graph open
downward. |
|
