1. Secondary Math 2
5.2 Falling Objects

2. Warm Up
Factor to solve. 6 𝑛 2 +5𝑛−6=0

3. Review Write 𝑓 𝑥 = 𝑥 2 +4𝑥−21 in… Factored form Vertex form
Then sketch the parabola

4. An “easier” way to write vertex form… Use mental math!
𝑓 𝑥 = 𝑥 2 −10𝑥+15

5. An “easier” way to write vertex form… Use mental math!
𝑓 𝑥 = 𝑥 2 +14𝑥−5

6. Write the factored form. Write the vertex form. Sketch it.
Standard 9:
Write the factored form.
Write the vertex form.
Sketch it.

7. Multiple choice tests can be rough…
I have graded 180+ students’ responses on similar questions that you see on the test. I know what mistakes you will make. Those options are on the multiple choice list… The average test score was 4/10. Yup. Why am I doing this, you ask? Because that dang ACT is designed the same way. They will try to trick you.

8. Test corrections
Some of you may be unhappy with your test score. Good news! You can do test corrections to earn half of that credit back. (If you scored a 60%, you can do test corrections to earn an 80%.) Test corrections must be done during R&R, before school, or after school. (Please let me know in advance if you plan on doing it before/after school.)

9. What you will learn
How to use quadratics to model falling objects.

10. Objects fall towards the earth at a rate of approximately 32 feet per second per second. Or, using our mathematical words, 32 feet per second squared.

11. A table representing 32 feet per second squared
Time (t) in seconds
Distance (feet) 1 32 2 64 3
128 4
256 t

12. Falling objects can be modeled by the following equation:
ℎ 𝑡 =−16 𝑡 2 + ℎ 0
Height of the object at any given time
The rate of gravity (this number will never change in your equations)
Starting height, or height at 0 seconds
Time in seconds

13. Let’s see how well this model works
Let’s see how well this model works. We are going to calculate how long it would take for an object dropped from the light on the ceiling to hit the ground. What do we need to measure?

14. Light height:
Function:
How do we solve the question: how long will it take for the ball to hit the ground?

16. Let’s check to see how accurate our model is.
Who has a stopwatch on their phone?
I need a volunteer to shout “go!”
When I hear “go!” I will let go of the ball. You need to start your stopwatches at “go!” and stop when you see/hear the ball hit the ground.

17. So…our model is not perfect.
Is it possible to create perfect models?
Why not?
If models aren’t perfect, then what’s the point?

18. Mrs. Anderson is standing on the edge of a cliff that is 200 feet tall
Mrs. Anderson is standing on the edge of a cliff that is 200 feet tall. She drops a watermelon off the cliff.
a) Sketch a picture

19. b) Write a function that represents this context.

20. c) How long will it take for the watermelon to hit the ground?

21. d) After 3.5 seconds, how far is the watermelon from the ground?

22. Airplanes typically fly at a height of 39,000 feet
Airplanes typically fly at a height of 39,000 feet. Let’s pretend you’re allowed to drop a bowling ball out of the plane (over the ocean).
a) Write a function that represents this context.

23. b) How long will it take for the bowling ball to reach the ground (ocean)?

24. c) After 10 seconds, how far from the ground is the bowling ball?

25. You are peering into an eerie well
You are peering into an eerie well. (It looks a lot like that one from that one movie.) You wonder how deep it is. You drop whatever is in your pocket into the well.
You hear it hit the water 13 seconds later.
a) How deep is the well?

26. b) Write a function to represent this context.

27. c) After 10 seconds, how far from the water is the object?

28. Test Corrections
To earn credit on the questions you missed, you will have to give me the correct answer AND show the work to back up that answer. Please do your test corrections on a lined sheet of paper, write the number of the problem you are working on, then SHOW ALL WORK to support your new answer. Staple your original test answer sheet to your test corrections, and turn it in.

29. Pink 1) D 2) C 3) C 4) B 5) B 6) A 7) A 8)D 9) B 10) E Yellow 1) B 2) D 3) B 4) C 5) E 7) B 8) C 9) A 10) D
Test answers
To earn back credit, show the work that proves the answer is correct.