Exploring the Equations of Parabolas
(a lesson plan using TI graphing calculators by Rebecca A. Zeier)
Objective:
After answering a variety of guided questions about the graphs of parabolas, students should be able to identify the different properties of parabolas solely by looking at the equations.
Activity:
Have the students work independently or in pairs to answer the following questions.
Directions:
Go to the graphing part of the TI Graphing Calculator and answer the following questions.
I. Graph y = x2
1. Describe the graph: ___________________________________________
______________________________________________________________
2. Now graph the following equations
y = x2 + 1
y = x2 + 3
3. Where does each graph cross the y-axis?
y = x2 ____________
y = x2 + 1 _________
y = x2 + 3 _________
4. Where do you think the graph of y = x2 + 6 will cross the y-axis? _________
5. Graph y = x2 + 6. Was your answer in number 4 correct? ________________
6. Make a conjecture. What does the “b” in the general equation y = x2 + b tell you about the graph of the line? ___________________________________________________________________________________
7. Does your conjecture hold true for the following equations?
y = x2 + 5 ________
y = x2 + 2 ________
Clear the graphs.
II. Graph (x + 1) 2
1. What happens? ____________________________________________________________________
2. Graph (x + 3) 2. What happens to this graph?______________________________________________
3. Describe what happens differently to these graphs from part I. __________________________________________________________________________________
4. Where do you think the graph of y = (x – 6) 2 will look like? __________________________________________________________________________________
5. Graph y = (x – 6) 2. Was your guess in number 4 correct? ___________________________________
6. Make a conjecture. What does the “d” in the general equation y = (x + d) 2 do to the graph?_____________________________________________________________________________
III. Graph the following equations on the same screen of your calculator:
y = (x + 1) 2 + 2
y = (x + 1) 2 + 5
y = (x + 1) 2 + 7
1. How are the graphs the same? _________________________________________________________
2. How do the graphs differ? ____________________________________________________________
IV. Graph the following equations on the same screen of your calculator:
y = (x + 3) 2 + 2
y = (x - 5) 2 + 2
y = (x + 7) 2 + 2
1. How are the graphs the same? __________________________________________________________
2. How do the graphs differ? _____________________________________________________________
V. Use your knowledge you have gained to predict what will be true about the following graphs:
y = (x - 3) 2 + 7 _______________________________________________________________________
y = (x + 7) 2 – 6 _______________________________________________________________________
y = x 2 + 3 ___________________________________________________________________________
y = (x + 0) 2 – 2 _______________________________________________________________________
VI. Graph the graphs from part V. Were you correct? __________________________________________
VII. Extra Credit: What do you think will happen when you graph the following equation?
y = - (x + 2) 2 + 7 _____________________________________________________________________