word problems.notebook May 27, 2016

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Jocelin Hillary Fletcher
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1 Word Problems: When solving word problems you can use vertex form, factored form or standard form to create an algebraic model of the situation. Use the form that is most helpful for the context of the problem. When you solve a quadratic equation, check that your solutions are admissible (that they make sense in the problem s context) PROJECTILES 1. The path of a thrown ball can be represented by Where h(d) is the height of the ball, in meteres, and d is the horizontal distance, in metres, from the person who threw the ball. a) What is the horizontal distance of the ball when it hits the ground?

3 2. A projectile is launched from a platform and its height (metres) is given as a function of time (seconds) as a) The time required for the projectile to reach the ground (h=0)

4 3. A baseball is hit at home plate and it s path is described by the function where h(t) is the height of the ball in metres and t is the time in seconds from when the ball was hit. a)what is the maximum height of the ball? b) How long did it take for the ball to reach its maximum height? c) What was the height of the ball when it was hit? d) How long did it take the ball to hit the ground

A ball is hit into the air with a bat. It height H (in cm) after t seconds is a. Which direction does the parabola open? b. What are the coordinates of the vertex?

5 A ball is hit into the air with a bat. It height H (in cm) after t seconds is a. Which direction does the parabola open? b. What are the coordinates of the vertex? What does it represent c. From what height was the ball hit d. How long does it take the ball to hit the ground?

6 A bridge has an arch of, where x is the horizontal distance and h(x) is the height of the bridge from the ground. Assuming that the beginning and end of the bridge is where the bridge meets the ground, what is the horizontal distance between the beginning and end of the bridge?

7 The path of one type of rocket at the Symphony of Fire is described by the function,, where h(t) is the height of the rocket, in metres, and t is the time, in seconds, since the rocket was fired. a. If the rocket did not explode, how long after would it hit the water?

8 A ball that was thrown into the air can be modelled by the quadratic function y = 4.9x 2 +49x where y is the height, in metres, above the ground, and x is the time, in seconds, after the ball was thrown. a. How long did it take the ball to reach the maximum height? b. Determine the maximum height that was attained by the ball? c. For how long was the ball in the air?

9 NOT ON YOUR HAND OUT The path of a basketball shot can be modelled by the function, where h(d) is the height of the basketball, in meteres, and d is the horizontal distance of the ball from the player, in metres. a) What is the horizontal distance of the ball when it hits the ground? b) At what height was the ball released from the players hand?

10 Extra Practice: The length of a soccer pitch is 20 m less than twice its width. The area of the pitch. is 6000 m 2. What at the dimensions of the pitch (field)

11 1. The length of a rectangle is 2 cm more than the width. The area of the rectangle is 20 cm 2. Find the dimensions of the rectangle to the nearest tenth of a cm. 2. The width of a rectangle is 2 m less than its length. The area of the rectangle is 48 m 2. What are the dimensions of the rectangle?

12 3. The area of a rectangle cribbage board is 270 cm 2, and the length is 17 cm greater than the width. What are the dimensions of the board?

13 4. A rectangular lawn measuring 8 m by 4 m is surrounded by a flower bed of uniform width the combined area of the lawn and the flower bed is 165 m 2. What is the width of the flower bed?

14 5. A landscaper is designing a rectangular garden, which will be 5.5 m wide by 6.5 m long. She has enough crushed rock to cover an area of 6.0 m 2 and she wants to make a uniform border of rock around the garden. How wide should the border be if she wants to use all of the crushed rock?

15 REVENUE QUESTIONS 1. A sporting goods store sells 90 ski jackets in a season for $275 each. Each $15 decrease in the price would result in 5 more jackets being sold. What is the price that would produce revenues of at least $17 500? How many jackets would be sold at that price?

16 2. A theatre company has 300 season ticket subscribers. The board of directors has decided to raise the price of a season ticket from the current price of $400. A survey of subscribers has determined that for every $20 increase in price, 10 subscribers would not renew their season ticket. What price of ticket would give the theatre a revenue of $ ? How many tickets are sold at that price?

17 3. A computer software program is sold to students for $20 each. Three hundred students are willing to buy it at that price. For every $5 increase, there are 30 fewer students willing to buy the software. What price of software would give the computer company a revenue of $7350? How many software programs are sold at this price?

18 Practice Questions: Page 419 #8, 13b, Page 407 #14a Page 428 #8, #10 TEST FRIDAY Extra help Thurs. Lunch and afterschool

19 4. Subtracting a number from its square gives 600. Find the number

a. Sketch the path of the diver by plotting the vertex, y-intercept, and additional points as needed.

a. Sketch the path of the diver by plotting the vertex, y-intercept, and additional points as needed. Algebra Applications of quadratic functions Name: 1. The path of a diver off a springboard is modeled by the function h( x) ( x 3) 3, where h is the height of the diver and x is the distance of the diver