Q&A > Math 20-2C8 - MODULE 3: LESSON 9 ASSIGNMENT.

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Math 20-2

C8 - MODULE 3: LESSON 9 ASSIGNMENT 15 Marks Please show your work.

1. A soccer player kicks a ball from the ground to a maximum height of 12 m. The high point in the trajectory of the ball occurs at a distance of 18 m from the kicker. On the downward path, another player heads the ball at a height of 2.2 m from the ground.

(4 marks)

a. Write a quadratic function that models the situation.

Answer: (18,12) vertex Y=a(x-h)2+k Y=a(x-18)2+12 0=a (0,18)2+12 0=a (-18)2+12 -12=324a -12/324 A=1/27 Y=-(1/27)(x-18)2+12

(4 marks)

b. How far from the kicker in the line of the trajectory must a player be to head the ball as described? Give the answer to two decimal places.

Answer: 2.2=(-1/27)(x-18)2 +12 -9.8=(-1/27)(x-18)2 264.6=(x-18)2 X=18+√264.6 X=18+16.2665 X=34.2665 X=34.27 meters

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Math 20-2 2. A retail electronics chain makes a profit of $14 on every MP3 player of a certain brand that the chain sells. Last month the company sold a total of 600 of these MP3 players nationwide.

The marketing department suspects that for every $1 decrease in price, an additional 100 players could be sold. The marketing department is interested in maximizing the gross profit on this item. gross profit  (profit on each MP3 player)(number of players sold) Let y equal the gross profit and x equal the number of dollars the MP3 players are discounted. The profit per MP3 player will then be

.

(2 marks)

a. Write a function to model this situation.

Answer: Y=(14-x)(600+100) =-100 +800x+8400

(4 marks)

b. What is the maximum gross profit based on these estimates? How many dollars must the price decrease in order to get that maximum gross profit?

Answer:

−b 2a

−800 2(−100)

=4 Max profit gross is 100(4)^2 +800(4) +8400 =10,000 dollars (1 mark)

c. How can you verify the solution?

Answer: Graphing calculator

Submit your completed assignment to Dropbox C8 by the deadline.

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