LESSON Problem Solving 5-4 Completing the Square Sean and Mason run out of gas while fishing from their boat in the ... c. Solve the equation by compl...
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Name LESSON
5-4
Date
Class
Problem Solving Completing the Square
Sean and Mason run out of gas while fishing from their boat in the bay. They set off an emergency flare with an initial vertical velocity of 30 meters per second. The height of the flare in meters can be modeled by h t ⴝ ⴚ5t 2 ⴙ 30t, where t represents the number of seconds after launch. 1. Sean thinks the flare should reach at least 15 meters to be seen from the shore. They want to know how long the flare will take to reach this height. a. Write an equation to determine how long it will take the flare to reach 15 meters. b. Simplify the function so you can complete the square. c. Solve the equation by completing the square.
15 ⫽ ⫺5t 2 ⫹ 30t t 2 ⫺ 6t ⫽ ⫺3 t ⫽ 0.6, 5.4
d. Mason thinks that the flare will reach 15 meters in 5.4 seconds. Is he correct? Explain.
Possible answer: He is partially correct. The flare will first reach 15 meters at 0.6 second after firing and then again at 5.4 seconds. (The function has two solutions.) e. Sean thinks the flare will reach 15 meters sooner, but then the flare will stay above 15 meters for about 5 seconds. Is he correct? Explain.
Possible answer: He is correct. The flare will first reach 15 meters at 0.6 second after firing. Also, the difference between 5.4 and 0.6 seconds (the two solutions) is 4.8 seconds, which is about 5 seconds. 2. Sean wants to know how high the flare will reach above the surface of the water. a. Write the function in vertex form, factoring so the coefficient of t 2 is 1.
h t ⫽ ⫺5 t 2 ⫺ 6t ⫹ 9 ⫹ 45
b. Complete the square using the vertex form of the function.
h t ⫽ ⫺5 t ⫺ 3 2 ⫹ 45 The constant term; 45 meters
c. How high will the flare reach? Choose the letter for the best answer.
4. The boys fire a similar flare from the deck 5 meters above the water level. Which statement is correct?
3. Use the vertex form of the function to determine how long after firing the flare it will reach its maximum height. A 3s
