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How do you find out how high an arrow might fly? For example

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.

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How do you find out how high an arrow might fly? For example

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  1. How do you find out how high an arrow might fly? For example If an arrow is shot at 50 m/s upwards, when will it be above a certain height?

  2. In this lesson you will learn how to create and solve inequalities by using a quadratic relationship

  3. Quadratic inequalities have a range of values that make the inequality statement true. x2 - x -12 ≤ 0 -3 ≤ x ≤ 4 -5? 0? 5?

  4. Not verifying answers after solving.

  5. 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?

  6. 1 ≤ t ≤ 4 h(t) = -10t2 + 50t 40 ≤ -10t2 + 50t 40 = -10t2 + 50t 0 = -t2 + 5t - 4 (-t+4)(t-1) = 0 5? 3? 0? t= 1, 4

  7. 1 ≤ t ≤ 4 40 ≤ -10t2 + 50t VERIFY: what do my answers mean? do they make sense?

  8. In this lesson you have learned how to create and solve quadratic inequalities by using a quadratic relationship

  9. 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?

  10. h(t) = -10t2 + 50t 60 ≥ -10t2 + 50t 60 = -10t2 + 50t t ≤ 2, t≥3 0 = -t2 + 5t - 6 (-t+2)(t-3) = 0 4? 2.5? 1? t= 2, 3

  11. 60 ≥ -10t2 + 50t t ≤ 2, t≥3 0 ≤t≤ 2, 3 ≤t≤ 5 VERIFY: what do my answers mean? do they make sense?

  12. Use this equation to investigate how far objects fall when dropped, according to time: h(t)= -10t2 • 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

  13. 1. 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?

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