MPM 2D QUADRATICS APPLICATIONS – REVIEW
1. A ball is shot into the air. Its height h, in meters, after t seconds is modeled by .
What is its maximum height? When will it land? How long will it take the ball to reach a height of 35m? (47.5m, 6.17 s, 1.46 s or 4.66 s)
2. The sum of the squares of 3 consecutive integers is 770. What are the integers? (15, 16, 17 or -17, -16, -15)
3. The vertical distance d (in cm) of the end of a robot arm above a conveyor belt is given by where t is the time in seconds. What height does the robot arm start at, and when does it return again to its starting height? (47cm, 8s). What is its minimum height? (15 cm)
4. The perimeter of a rectangular window is 8.4 m and its area is 3.8 m2. What are the dimensions? (1.32 m x 2.88 m)
5. The difference between the length of a hypotenuse and the length of the next longest side of a right triangle in 4.0 cm. The difference between the lengths of the two perpendicular sides is also 3.0 cm. Find all three side lengths. (14.5 cm, 11.5 cm, 18.5 cm)
6. What is the height of the parabolic arch at 0.5 m from one of the edges given the arch is 1.6 m wide and has a maximum height of 1.28 m (0.78 m).
7. A music concert venue usually gets 500 visitors to pay an entrance cost of $10. Using a survey they determine that every increase in price of $0.75 will cause 25 fewer people to attend. What should their entrance cost be to maximize revenue? What is the revenue? ($12.50, $5208.33)
8. Use 3 different methods to show that the relation has two real distinct roots (zeroes).
9. What value(s) of m will make the graphs of the relation have only one real root? (19.42 or -7.42)
10. A door has dimensions 0.9 m wide and 2.10 m high. The door will have a rectangular hole in it to allow for a decorative panel to be placed inside. The decorative panel has an area of 1.20 m2. Around the edges of decorative panel the door should have a uniform width on the top and sides, and twice this width at the bottom. What are the dimensions of the hole in the door? (answer to follow)
11. In gym class, Shafiq throws a baseball on the back field. The path of the baseball can be modeled by the relation where h is the height of the ball, in meters, and d is the horizontal distance of the ball, in meters. Describe all the key information about the path of the baseball.
12. Two girls are 5 m apart and are turning a skipping rope. The rope keeps a parabolic shape as it is turned. The girls keep the ends 1.2 m off the ground at the ends, and the rope just touches the ground as it turns. How many 1.6 m tall girls can jump rope if they must stay 1 m and the rope must be able to pass over their heads as they stand upright? (answer to follow)