Name: ______________________________
MPM 2DI Unit 4 – Quadratic Relations Assignment
This assignment is due on Tuesday May 3 at the beginning of class. No assignments will be accepted after the
end of the day on Tuesday May 3. Complete solutions and thorough explanations are required for all questions.
Only neat and organized solutions will receive full marks. Feel free to use your notes and ask questions.
1. a) Relation A = {(3, 2), (5, 6), (6, 8), (3, -2), (6, -4)}
i) State the domain and range
b) Relation B = {(7, 1), (5, 1), (-4, 1), (-1, 1)}
i) State the domain and range
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c) Is this relation x  y  31 a function? Explain.
d) Is this relation y  2x  1 a function? Explain.
2.
ii) Is this relation a function? Explain.
ii) Is this relation a function? Explain.
A soccer ball is kicked from the ground level. When it has traveled 35 m horizontally, it reaches its maximum height of 25
m. The soccer ball lands on the ground 70 m from where it was kicked.

a) Model
 this situation with a relation in the form y  a( x  h)  k .
b) What is the soccer ball’s height when it is 50 m from where it was kicked?
3.
4.
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A football is punted into the air. Its height h, in metres, after t seconds is h  4.9(t  2.4)  29.
a) What was the height of the ball when it was kicked?
b) What was the maximum height of the ball?
c) How high was the ball after 2 s? Was it going up or down at that time? Justify your answer.
d) When does the ball hit the ground?

2
If a pistol bullet is fired vertically at an initial speed of 100 m/s, the height in metres after t seconds is given by
h  100t  5t 2 . Find the maximum height attained by the bullet.

5.
An architect has designed a modern building that is to be supported by a steel arch shaped like a parabola. This parabola can
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be modelled by the relation y  0.025x  2x , where y represents the height of the arch and x represents the distance
along the base, both in metres.
a) Convert the relation to vertex form.
b) What is the highest point on the parabolic arch?
c) What is the width
 of the arch at its base?
6.
Hermione’s mother owns a manufacturing company that produces key rings. Last year, she collected data about the number
of key rings produced per day and the corresponding profit. The data can be modelled by the relation
P  2k 2  12k 10 , where P is the profit in thousands of dollars and k is the number of key rings in thousands.
a) How many key rings must be produced for the maximum profit?
b) What is the maximum profit?
c) Graph this relation.
7.
Hiroshi is trying out for the position of kicker on the football team. He wants to know at what angle he should kick the ball
for maximum distance. He has used a machine that kicks footballs with constant velocity but at varying angles. Hiroshi has
collected some data and used quadratic regression on his graphing calculator to determine that the relation between angle and
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distance is given by the equation d  0.1a  8.5a  40 where a is the angle in degrees, and d is the distance in metres.
a) If Hiroshi kicks the ball at an angle of 60°, how far will the ball go?
b) Determine the vertex of the parabola.
c) Which angle gives the maximum distance?
8.
9.
A research study has 
shown that 500 people attend a PHS football game in a tournament when the admission price is $2. In
the championship game, the price will be considered for an increase: for every 20¢ increase, 20 fewer people will attend.
What price will maximize the revenue? What is the value of the maximum revenue?
A rectangular field is to be enclosed with 600 m of fencing. What dimensions will produce a maximum area?
10. A field is bounded on one side by a river. The field is to be enclosed on three sides by a fence, to create a rectangular
enclosure. The total length of fence to be used is 100 m. What dimensions will produce a maximum area?
11. What is the maximum area of a triangle having 15 cm as the sum of its base and height?
Bonus:
12. A rectangle has perimeter P. Find the maximum possible area of the rectangle. (Answer: P2/16 units2, you have to explain why)