Parabola Investigation
Algebra II
Name:
1.
2.
3.
4.
Go to http://www.shodor.org/interactivate/activities/ConicFlyer/
In the activity box, change the drop down menu to be “Vertical Parabola”
Copy the equation written under the drop down menu: _____________________________
Use the slider at the bottom of the screen to make a = 1. Complete the table and sketch the graph.
Equation:
Vertex Point
x-intercepts
y-intercept
5. There are three slides below the graph window. Which slider do you move to shift the parabola’s
vertex point left or right? [AFTER DOING THIS, RESET THE SLIDERS TO BE A = 1, H =
0, K = 0]
a. Move the appropriate slider until the graph’s vertex point is at (2, 0).
Write the equation: ______________________
b. Move the appropriate slider until the graph’s vertex point is at (-5, 0).
Write the equation: ______________________
c. Move the appropriate slider until the graph’s vertex point is at (4, 0).
Write the equation: _____________________
6. Which slider do you move to shift the parabola’s vertex point up or down? [AFTER DOING
THIS, RESET THE SLIDERS TO BE A = 1, H = 0, K = 0]
a. Move the appropriate slider until the graph’s vertex point is at (0, 5).
Write the equation: _______________________
b. Move the appropriate slider until the graph’s vertex point is at (0, -3).
Write the equation: ______________________
c. Move the appropriate slider until the graph’s vertex point is at (0, 2.6).
Write the equation: _____________________
[AFTER DOING THIS, RESET THE SLIDERS TO BE A = 1, H = 0, K = 0]
7. Move TWO sliders until the graph’s vertex point is…
a. (2, 4) equation: _______________________
b. (-1, 6) equation: _______________________
c. (-3, -5) equation: _______________________
[AFTER DOING THIS, RESET THE SLIDERS TO BE A = 1, H = 0, K = 0]
8. “Vertical Stretch” means that the parabola looks narrow and “Vertical Compression” means that
the parabola is wide. Which slider do you move to make the parabola become vertically stretched
or compressed? [AFTER DOING THIS, RESET THE SLIDERS TO BE A = 1, H = 0, K = 0]
a. Move the appropriate slider until the parabola is stretched. Write the equation of THREE
DIFFERENT stretched parabolas.
Equation 1: _________________________
Equation 2: _________________________
Equation 3: _________________________
b. Move the appropriate slider until the parabola is compressed. Write the equation of
THREE DIFFERENT compressed parabolas.
Equation 1: ________________________
Equation 2: ________________________
Equation 3: ________________________
c. Move the appropriate slider until the parabola is upside down. Write the equations of
THREE DIFFERENT upside down parabolas.
Equation 1: _____________________
Equation 2: ____________________
Equation 3: _____________________
[AFTER DOING THIS, RESET THE SLIDERS TO BE A = 1, H = 0, K = 0]
9. Move THREE SLIDERS until the following conditions are met…
a. Stretched AND vertex point at (2, 5) equation _________________________
b. Compressed AND vertex point at (-1, -3) equation ______________________
c. Upside down AND vertex point at (4, -2) equation ______________________
Please take the time to complete the following conjectures:
How would you change the equation
…open upside down?
…stretched?
… compressed?
… shift right?
…shift left?
…shift up?
…shift down?
to make the parabola…
Match each equation from column 1 with a description from column 2. Draw an accurate sketch of the
graph in column 3.
Column 1: The Letters
A:
Column 2: The Numbers
#1: Shifted 4 right and 3 down
Column 3
Matching letter:
Matching number:
Sketch:
B:
#2: Upside down and shifted 3
down
Matching letter:
Matching number:
Sketch:
C:
#3: Upside down and stretched
Matching letter:
Matching number:
Sketch:
D:
#4: Compressed, shifted 1 left,
and shifted 2 up
Matching letter:
Matching number:
Sketch:
E:
#5: Compressed and shifted 4 left
Matching letter:
Matching number:
Sketch: