MPM 2D Grade 10
GRAPHS of QUADRATIC RELATIONS
Chapter Test
1.
State whether each set of ordered pairs represents a function. a) {(2, 4), (3, 5), (7, 9), (2, −5), (3, −7)} b) {(5, 4), (4, 3), (3, 2), (2, 1), (1, 0)} c) {(−1, 6), (0, −6), (1, −6), (2, −6) }
2. Sketch the graph of each parabola and state the direction of opening, the coordinates of the vertex, the equation of the axis of symmetry, the domain and range, and maximun or minimum value. a) 𝑦 = 𝑥 2 − 1

Direction of opening: ______
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Domain: _________________
Range: __________________
Maximun or minimum value: ___________________________ b) 𝑦 = −𝑥 2 + 5
Direction of opening: ______
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Domain: _________________

Range: __________________
Maximun or minimum value: ___________________________
3.
Determine any x -intercepts, to the nearest tenth. a) 𝑦 = 𝑥 2 + 3 b) 𝑦 = −𝑥 2 + 10 c) 𝑦 = 8 − 3𝑥 2

4. Without sketching each parabola, state the direction of opening, how the parabola is stretched or shrunk, if at all, the coordinates of the vertex, the equation of the axis of symmetry, the domain and range, and maximun or minimum value. a) 𝑦 = (𝑥 + 3) 2 − 1
Direction of opening: ______
Vertical stretch/shrink: _________________
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Domain: _________________
Range: __________________
Maximun or minimum value: ___________________________ b) 𝑦 = −2(𝑥 − 5) 2 − 2
Direction of opening: ______
Vertical stretch/shrink: _________________
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Domain: _________________
Range: __________________
Maximun or minimum value: ___________________________

c) 𝑦 = −0.5(𝑥 + 2) 2 + 3
Direction of opening: ______
Vertical stretch/shrink: _________________
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Domain: _________________
Range: __________________
Maximun or minimum value: ___________________________
5.
Determine any x -intercepts, to the nearest tenth. a) 𝑦 = 2(𝑥 + 2) 2 − 9 b) 𝑦 = −(𝑥 − 2) 2 + 3

6.
Write each function in the form 𝑦 = 𝑎(𝑥 − ℎ) 2 + 𝑘 . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph. a) 𝑦 = 𝑥 2 + 8𝑥 + 8
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Points: ( , ) , ( , ) , ( , )

b) 𝑦 = −𝑥 2 − 10𝑥 − 4
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______
Points: ( , ) , ( , ) , ( , )

7.
Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range. a) 𝑦 = 𝑥 2 − 10𝑥
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______ x -intercepts: __________________________ y -intercept: _________
Range: ______________________

b) 𝑦 = −𝑥 2 − 6𝑥 − 10
Coordinates of the vertex: ( , )
Equation of the axis of symmetry: _______ x -intercepts: __________________________ y -intercept: _________
Range: ______________________

8.
Find the coordinates of the vertex. a) 𝑦 = 2𝑥 2 + 12𝑥 + 13 b) 𝑦 = −3𝑥 2 + 24𝑥 − 50

9.
Sketch the graph of each of the following quadratic functions by writing it in the form 𝑦 = 𝑎𝑥(𝑥 − 𝑠) + 𝑡 . a) 𝑦 = 𝑥 2 − 8𝑥 + 5

b) 𝑦 = −2𝑥 2 + 4𝑥 − 3

c) b)
10.
Use finite differences to determine whether each function is linear, quadratic, or neither. a) x
0
1
2
3 y
-1
1
7
17 x
2
4
6
8 y
0
4
8
12 x
1
2
3
4 y
1
16
81
256

11.
The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modelled by the function ℎ = −5.25(𝑡 − 4) 2 + 86 a) What was the maximum height of the flare? b) What was its height when it was fired? c) How many seconds after it was fired did the flare hit the water, to the nearest second?

12.
The captain of a riverboat cruise charges $36 per person, including lunch. The cruise averages 300 customers a day. The captain is considering increasing the price. A survey of customers indicates that for every $2 increase, there would be 10 fewer customers. What increase in price would maximize the revenue?

13.
The diagram show the first four rectangles in a pattern. a) Write an equation that relates the area, A , of each rectangle to its width, w . b) Find the area of the 25 th rectangle in the pattern.

14.
Draw a scatter plot for each table of values and fit an equation of a quadratic function to each scatter plot. a) x
2
1
0
-1
-2 y
2
-1
-2
-1
2

b)
0
-1
-3 x
3
1 y
-5
2
3
2
-7

15.
A cattle farmer wants to build a rectangular fenced enclosure divided into three rectangular pens, as shown in the diagram. A total length of 120 m of fencing material is available. Find the overall dimensions of the enclosure that will make the total area a maximum.
Explain and justify your reasoning.