1. writing equations of quadratic equations unit 3

2. KEY CONTENT:
A-CED.A.2: I can create equations and inequalities in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels.
F-BF.A.1b: I can write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations.
F-IF.B.6: I can calculate and interpret the average rate of change of a function over a specified interval.

3. Today I will learn how to write a quadratic equation given specific information.

4. Mini Lesson #1 writing an equation of a quadratic function using a point on the graph and the x-intercepts
PART A:
Video – Take Notes - (0:00 - 2:47)
PART B:
In the example from the video above, what would the final equation look like if you rewrote it in standard form?

5. Mini Lesson #1 PART A: Write the equation of the parabola in
intercept form/factored form.

6. Mini Lesson #1
PART B:
What would the final equation look like if you rewrote it in standard form?

7. Independent practice Example 1
Write an equation of the parabola
in intercept form.

8. Independent practice Example 1
Write an equation of the parabola
in intercept form.

9. Independent practice Example 2
Write an equation of the parabola in factored form given it has
x-intercepts of 12 and – 6 and passes through (14,4) .

10. Independent practice Example 2
Write an equation of the parabola in intercept form given it has
x-intercepts of 12 and – 6 and passes through (14,4) .

11. Independent practice Example 3
Write an equation of the parabola in standard form given it has
x-intercepts of 9 and 1 and passes through (0, -18) .

12. Independent practice Example 3
Write an equation of the parabola in standard form given it has
x-intercepts of 9 and 1 and passes through (0, -18) .

13. Guided practice Example 4
A meteorologist creates a parabola to
predict the temperature tomorrow,
where x is the number of hours after midnight and y is the temperature (in degrees Celsius).
Part A: Write a function that models the temperatures over time.

14. Guided practice Example 4
Part A: Write a function that models the temperatures over time.

15. Guided practice Example 4
Part B: What is the coldest temperature?

16. Guided practice Example 4
Part B: What is the coldest temperature?
The coldest temperature is the minimum
value on the parabola.

17. Guided practice Example 4
Part C: When is the coldest time of day?

18. Guided practice Example 4
Part C: When is the coldest time of day?
It occurs at 14 hours after midnight.
The coldest temperatures of – 10˚ C occurs at 2 p.m.

19. Guided practice Example 4
Part D: What is the average rate of change in temperature over the interval in which the temperature is decreasing?

20. Guided practice Example 4
Part D: What is the average rate of change in temperature over the interval in which the temperature is decreasing?
The vertex (14, -10) has already been identified part b. The function is decreasing on the interval (0,14).
Calculate the average rate of change: (0,10) (14,-10)

21. Guided practice Example 4
Part D: What is the average rate of change in temperature over the interval in which the temperature is decreasing?
The average rate of change on the interval
(0,14) is -1.4 degrees C˚ per hour.

22. Guided practice Example 4
Part E: What is the average rate of change in temperature over the interval in which the temperature is increasing?

23. Guided practice Example 4
Part E: What is the average rate of change in temperature over the interval in which the temperature is increasing?
The vertex (14, -10) has already been identified part b. The function is increasing on the interval (14,24).
Calculate the average rate of change:
(14,-10)(24,0)

24. Guided practice Example 4
Part E: What is the average rate of change in temperature over the interval in which the temperature is increasing?
The average rate of change on the interval
(14,24) is 1 degree C˚ per hour.

25. Guided practice Example 4
Class Discussion: Why are the endpoints of the increasing and decreasing intervals enclosed by parenthesis and not brackets?

26. Guided practice Example 4
Class Discussion: If parabolas are always symmetrical, why are your calculations for the rates of change on the increasing and decreasing intervals of this parabola not equivalent?

27. Guided practice Example 4
Part F: Compare the average rate of change for both intervals within the context of the problem.

28. Guided practice Example 4
Part F: Compare the average rate of change for both intervals within the context of the problem.
The average rate of change at which the temperature decreases from midnight to
2 p.m. is greater than the average rate at which it increases from 2 p.m. to midnight.
In other words, the temperature decreases for a longer period of time than it increases on this specific time frame.

29. Guided practice Example 4
Part G: If the y – intercept was half its value, how would that change your answer to part A and B?

30. Guided practice Example 4
Part G: If the y – intercept was half its value, how would that change your answer to part A and B?
The equation would change to
and the coldest temperature would
be – 5˚ C.

31. Independent practice Example 5
A meteorologist creates a parabola to
predict the temperature the day after tomorrow, where x is the number of hours after midnight and y is the temperature (in degrees Celsius).

32. Independent practice Example 5
Part A: Write a function that models the temperatures over time.
Part B: What is the coldest temperature?

33. Independent practice Example 5
Part A: Write a function that models the temperatures over time.
Part B: What is the coldest temperature?

34. Independent practice Example 5
Part C: What is the average rate of change on the interval in which the temperature is decreasing? increasing? Compare the average rates of change.

35. Independent practice Example 5
The function decreasing on the interval
(0,13.5) and the average rate of change on this interval is degrees C˚ per hour.
The function increasing on the interval
(13.5, 21) and the average rate of change on this interval is degrees C˚ per hour.
Thus the average rate of change at which the temperature decreases is greater than the average rate of time on which it increases in this time frame.

36. Mini Lesson #2 writing an equation of a quadratic function using three random points on the parabola.
PART A:
Review how to solve a system of three equations using the RREF method on the calculator.

37. Mini Lesson #2 writing an equation of a quadratic function using three random points on the parabola.
PART A:
Review how to solve a system of three equations using the RREF method on the calculator.

38. Mini Lesson #2 writing an equation of a quadratic function using three random points on the parabola.
PART B:
Video – Take Notes - (5: :15)

39. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

40. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

41. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

42. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

43. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

44. Guided Practice Example 6
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 2), and (3, - 4).

45. independent Practice Example 7
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 4), and (3, - 4).

46. independent Practice Example 7
Write an equation in standard form of the parabola passing through the points (1, - 2), (2, - 4), and (3, - 4).

47. independent Practice Example 8
Steph Curry shoots the basketball. The basketball follows a parabolic path that can be modeled by the equation below.
If the center of the hoop is located at (12,10), will his shot go through the hoop?

48. independent Practice Example 8
How did you achieve your answer?

49. independent Practice Example 8
Klay Thompson shoots the basketball. The table to the right models the parabolic path of the ball as it heads towards the hoop.
If the center of the hoop is located at (12,10), will his shot go through the hoop?

50. independent Practice Example 8
How did you achieve your answer?