Applications of Completing the Square (Lesson).notebook
Applications of Completing the Square (Lesson).notebook
y = ‐2x2 ‐ 4x + 1
WARM-UP
(1, 3)
Find the vertex of the quadratic using partial factoring.
y = ‐2x2 ‐ 4x + 1
HOMEWORK TAKEUP
(‐6, 0)
(0, 0)
Pg. 116, #2f Find the vertex by partial factoring and the zeros by factoring. Sketch the parabola. y = 2x2 + 12
(‐3, ‐18)
Applications of Completing the Square (Lesson).notebook
UNIT #3: Quadratic Functions
OTHER HOMEWORK TAKEUP Pg. 116 #2,3
Applications of Completing the Square Learning Goal: I will learn how to solve application questions using the completing the square method.
Lesson: Applications of Completing the Square
a) Maximum height of flare
Example 1: The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function
a) What is the maximum height of the flare? b) What was its height when it was fired? c) How many seconds after it was fired did the flare hit the water?
Therefore, the maximum height of the flare is 86m.
Applications of Completing the Square (Lesson).notebook
(4, 86) b) Height of flare when it was fired:
When the flare was fired, time = 0s
Therefore, the height of the flare at firing is 2m.
c) How many seconds after it was fired did the flare hit the water?
When the flare hits the water, h = 0m.
Example 2: A rectangular field is to be enclosed by 400 m of fence. a) What dimensions will give a maximum area? b) What is the maximum area?
200‐x x
Therefore, the flare hit the water at 8.05 s.
Area = x(200‐x) Expand first! = ‐x2 + 200x Complete square = ‐(x2 ‐ 200x + 10000 ‐ 10000) = ‐(x ‐ 100)2 + 10000 Therefore the maximum area is 10000 m2. It occurs at x = 100 m. Therefore, the dimensions are 100m x 100m.
Applications of Completing the Square (Lesson).notebook
UNIT 3: Quadratic Functions Applications of Completing the Square
Learning Goal: I will learn how to solve word applications using the completing the square method.
Success Criteria: To be successful, I must be able to.... • Complete the square to find the max or min value in a word application • Substitute values and solve for the appropriate variable
Practice Work Pg. 116 #4 ‐ 10 Tomorrow: Radicals, Completing the Square, Partial Factoring Assessment
y = ‐2x2 ‐ 4x + 1
WARM-UP
(1, 3)
Find the vertex of the quadratic using partial factoring.
y = ‐2x2 ‐ 4x + 1
HOMEWORK TAKEUP
(‐6, 0)
(0, 0)
Pg. 116, #2f Find the vertex by partial factoring and the zeros by factoring. Sketch the parabola. y = 2x2 + 12
(‐3, ‐18)
Applications of Completing the Square (Lesson).notebook
UNIT #3: Quadratic Functions
OTHER HOMEWORK TAKEUP Pg. 116 #2,3
Applications of Completing the Square Learning Goal: I will learn how to solve application questions using the completing the square method.
Lesson: Applications of Completing the Square
a) Maximum height of flare
Example 1: The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function
a) What is the maximum height of the flare? b) What was its height when it was fired? c) How many seconds after it was fired did the flare hit the water?
Therefore, the maximum height of the flare is 86m.
Applications of Completing the Square (Lesson).notebook
(4, 86) b) Height of flare when it was fired:
When the flare was fired, time = 0s
Therefore, the height of the flare at firing is 2m.
c) How many seconds after it was fired did the flare hit the water?
When the flare hits the water, h = 0m.
Example 2: A rectangular field is to be enclosed by 400 m of fence. a) What dimensions will give a maximum area? b) What is the maximum area?
200‐x x
Therefore, the flare hit the water at 8.05 s.
Area = x(200‐x) Expand first! = ‐x2 + 200x Complete square = ‐(x2 ‐ 200x + 10000 ‐ 10000) = ‐(x ‐ 100)2 + 10000 Therefore the maximum area is 10000 m2. It occurs at x = 100 m. Therefore, the dimensions are 100m x 100m.
Applications of Completing the Square (Lesson).notebook
UNIT 3: Quadratic Functions Applications of Completing the Square
Learning Goal: I will learn how to solve word applications using the completing the square method.
Success Criteria: To be successful, I must be able to.... • Complete the square to find the max or min value in a word application • Substitute values and solve for the appropriate variable
Practice Work Pg. 116 #4 ‐ 10 Tomorrow: Radicals, Completing the Square, Partial Factoring Assessment
