how do you find out how high an arrow might fly? for example
DESCRIPTION
How do you find out how high an arrow might fly? For example I f an arrow is shot at 50 m/s upwards, when will it be above a certain height?. In this lesson you will learn how to create and solve inequalities by using a quadratic relationship. - PowerPoint PPT PresentationTRANSCRIPT
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How do you find out how high an arrow might fly?
For exampleIf an arrow is shot at 50 m/s
upwards, when will it be above a certain height?
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In this lesson you will learn how to create and solve
inequalitiesby using a quadratic
relationship
![Page 3: How do you find out how high an arrow might fly? For example](https://reader036.vdocuments.site/reader036/viewer/2022062520/56816145550346895dd0c00b/html5/thumbnails/3.jpg)
Let’s Review
x2 - x -12 ≤ 0
-5? 5?0?-3 ≤ x ≤ 4
Quadratic inequalities have a range of values that make the inequality statement true.
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A Common Mistake
Not verifying answers after solving.
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Core Lesson
We will investigate the following problem: An arrow is shot straight upwards; its height
(in meters) above the ground can be modeled with an equation: h(t) = -10t2 + 50t
During what time(s) will the arrow be above 40 meters above the ground?
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Core Lesson
h(t) = -10t2 + 50t40 ≤ -10t2 + 50t40 = -10t2 + 50t
0 = -t2 + 5t - 4(-t+4)(t-1) = 0t= 1, 4 0? 5?3?
1 ≤ t ≤ 4
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Core Lesson
40 ≤ -10t2 + 50t
1 ≤ t ≤ 4
VERIFY: what do my answers mean? do they make sense?
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In this lesson you have learned how to create and solve quadratic inequalitiesby using a quadratic
relationship
![Page 9: How do you find out how high an arrow might fly? For example](https://reader036.vdocuments.site/reader036/viewer/2022062520/56816145550346895dd0c00b/html5/thumbnails/9.jpg)
Guided Practice
We will investigate the following problem: An arrow is shot straight upwards; its height
(in meters) above the ground can be modeled with an equation: h(t) = -10t2 + 50t
During what time(s) will the arrow be below 60 meters above the ground?
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Guided Practice
h(t) = -10t2 + 50t
60 = -10t2 + 50t60 ≥ -10t2 + 50t
0 = -t2 + 5t - 6(-t+2)(t-3) = 0t= 2, 3 1? 4?2.5?
t ≤ 2, t≥3
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Guided Practice
60 ≥ -10t2 + 50t
VERIFY: what do my answers mean? do they make sense?
t ≤ 2, t≥30 ≤ t ≤ 2, 3 ≤ t ≤ 5
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Extension Activities
a. Use this equation to investigate how far objects fall when dropped, according to time: h(t)= -10t2
b. Go back to the practice problems and find the maximum height of the arrow. You can also investigate at what time it returns to the ground, etc
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Quick Quiz1. A flare is launched from a stranded boat to call for help; the height of the flare is modeled by the equation: h(t)=-10t2 + 100t When will the flare be above 160 m, so the coast guard can see it?2. Angela opened up a new restaurant, and predicted that its profit could be modeled with the equation: p(t) = 1125(t-1)2 – 10,125 During what time spans will Angela’s restaurant NOT make a profit?