Lesson 1: What is a Parabola?

Transcription

1 Lesson 1: What is a Parabola? Parabola Vocabulary Write the defintion of the given word. Label #3-6 on the graph. 1. Parabola: Name Class Date 2. Trajectory: 3. Zeros: 4. Axis of Symmetry: 5. Vertex: Online Graphing Calculator Determine whether each equation graphs a parabola by entering the equation in the online graphing calculator. Write Yes if it does. If it does not graph a parabola, write No and describe why it is not a parabola based on the definitions above. 6. y=x 12. y=x y=x y=4x y=2x y=3x 2-5x+1 9. y=(x-1)(x+2) 15. y=x y=4(x-1)(x+2) 16. y=(x-1)(x+3)(x-4) 11. y=x 2 Answer the following questions. 17. What do all the equations that graph parabolas have in common that sets them apart from the other equations? In other words, how can we tell if an equation is a parabola without seeing the graph? 18. Based on your answer to #17, write your own parabola equation. (Check that it is a parabola using the online graphing calculator.)

2 Lesson 2: Pilot Training Parabola KWL Know Want to Know Learned Pilot Training 1 Questions 19. What is the difference between the graph of a parabola with a positive coefficient and one with a negative coefficient? (A coefficient is the number in front of a variable.) 20. Given your answer to #19, will the coefficient of a trajectory be positive or negative? 21. What happens to the parabola when the coefficient is between a positive and negative number, in other words, when the coefficient is zero? 22. What happens to the coefficient as the parabola gets thinner? 23. What happens to the coefficient as the parabola gets thicker? Pilot Training 2 Questions 24. Enter the following pairs of numbers in the blanks of the interactive and watch what happens to the parabola: a) 1 and 2 b) -5 and 4 c) -3 and 0 What is the relationship between the numbers entered and the graph? (Use the proper vocabulary where applicable.) 25. What happens when you enter the same number into each blank? In other words, how is this situation different than when you enter two different numbers (like you did for #23)?

3 Lesson 3: Evaluating Expressions Warm-up Procedure for Evaluating Expressions Evaluating Expressions Examples 28. Find y when x=2 if y=x 2 +2x Find y when x=4 if y= ½ x 2 +3x 29. Find y when x=-3 if y=4x 2-6x+2

4 Lesson 4: Parabola Maximums & Minimums Maximum & Minimum Problems Find the vertex (maximum or minimum) of each parabola, then sketch the graph. 31. h=-d 2 +4d-3. The zeros are at d=1 and d= h=d 2 +2d. The zeros are at d=-2 and d= h=d 2 -d-6. The zeros are at d=3 and d= h=d 2-2d-48. The zeros are at d=-6 and d= h=d 2 +7d+6. The zeros are at d=-6 and d=-1..

5 Lesson 5: Velocity Make a list of everything you know about velocity. Velocity formula:.

6 Velocity Problems Find the average velocity of the projectile. Round answers to the nearest thousandth. 36. A projectile takes 45 seconds to fly 30 meters. What is the average velocity of the projectile in m/s? 37. A projectile takes 1 minute to fly 50 meters. What is the average velocity of the projectile in m/s? 38. A projectile s trajectory is shown in the graph to the right. The x-axis represents the distance it traveled in meters, and the y-axis represents the height of the projectile in meters. The projectile was airborne for 10 seconds. What was the average velocity of the projectile in m/s? 39. A rocket s flight is shown in the graph to the right. The projectile was in the air for 2 minutes. What was the average velocity in ft/s? 40. The zeros of a rocket s trajectory are at x=0 meters and x=5 meters. It s flight took 5 seconds. What was its average velocity in m/s? Slow-Motion Projectile Video 41. Label the graph of the projectile with the following information (There may be more than one location for each question): a. Where is the velocity highest? In other words, where is the projectile traveling the fastest? b. Where is the velocity the lowest? Velocity Homework Problems 42. The trajectory of a projectile s flight passes through the points (3,0) and (10,0) where the axis of the graph are measured in meters. The projectile s flight lasts 45 seconds. What is the average velocity in m/s? 43. The path of a ball thrown in the air is graphed, and the zeros of the graph are at x=4 meters and x=14 meters. The ball is in the air for 12 seconds. What is the average velocity of the ball in m/s?

7 Lesson 6: Understanding Formulas Warm-Up: Novel Ideas 44. Write down in the left column everything you can remember about velocity, momentum, and force. Understanding Formulas Write the formulas for quantities in the left column using the variables in the box to the right. Variables v = velocity p = momentum F = force d = distance t = time m = mass a = acceleration Math Experiment Guidelines Keep the variable you are not testing. Try two different values for the variable you are and observe what happens to the.

8 Postcard to an Absent Student 45. Summarize today s lesson. What are the two most important things a student who missed today s lesson would need to know? Homework A=v/t where a = acceleration, v = velocity, and t = time. Answer the following questions. 46. When the velocity increases, what is the effect on the acceleration? 47. When the time increases, what is the effect on the acceleration?