MATHEMATICS
Quadratic equations and Functions - Sheet
Date: 24th March 2009
Student name:
Class: MYP 4
1. Draw the graphs of the following function;
And then state the following:
i) The y-intercept
ii) The zeros of the equation
iii) The equation of the axis of symmetry
iv) The coordinates of the vertex and whether it is a maximum or minimum
point
2.
The diagram shows part of the graph with equation y = x2 + px + q. The graph cuts the
x-axis at –2 and 3.
y
6
4
2
–3
–2
–1
0
1
–2
–4
–6
Find the value of
(a)
Parabola sheet
p;
(b)
q.
Page 1 of 6
2
3
4
x
3. The diagram shows the parabola y = (7 – x)(l + x). The points A and C are the x-intercepts
and the point B is the maximum point.
y
B
A
0
C
x
Find the coordinates of A,B and C
4. For each of the sketches below, write down the corresponding equation in the form of
y  ax 2  bx  c

Parabola sheet
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5.
The diagram shows the graph of the function y = ax2 + bx + c.
y
x
Complete the table below to show whether each expression is positive, negative or zero.
Expression
positive
negative
zero
a
c
b
6. For the following equations; find the coordinates of
i- the point where the line cuts the y-axis,
ii- the points where the line cuts the x-axis,
iii- any maximum or minimum points.
iv- Hence sketch the graph.
a) y  x 2  5x  4
b) y  4  3x  x 2
7. Sketch the following graphs

a)
b)
c)
d)

8. Solve the following equations.
a)
and
b)
and
c)
and
d)
and
e)
and
Parabola sheet
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9. The hourly profit ($P) obtained from operating a fleet of n taxis is given by
P(n) = 84n - 45 - 2n2.
a) What number of taxis gives the maximum hourly profit?
b ) What is the maximum hourly profit?
c ) How much money is lost per hour if no taxis are on the road?
10. The temperature
Celsius in a greenhouse t hours after dusk (7:00 pm) is given by
, (t≤ 20).
a) What was the temperature in the greenhouse at dusk?
b ) At what time was the temperature at a minimum?
c) What was the minimum temperature?
11. A vegetable gardener has 40 m of fencing to enclose a rectangular garden plot where one side is
an existing brick wall. If the width is x m as shown:
2
a) Show that the area (A) enclosed is given by A  2 x  40 x m2
b ) Find x such that the vegetable garden has maximum area.
c ) What is the maximum area?
Parabola sheet
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Answers.
1. i- (0,-3) ii- x = -1, -3 iii- x = -2 iv- (-2,1), maximum
5
y
4
3
2
1
x
-5
-4
-3
-2
-1
1
2
3
4
5
-1
-2
-3
-4
-5
2. a) -1
b) -6
3. A(-1,0), B (3,16), C( 7,0)
4. a)
b)
c)
d)
e)
f)
5. a, negative
b, positive
c, negative
6. a) i- (0,4) ii- (1,0), (4,0) iii- (2.5,-2.25)
5
y
4
3
2
1
x
-2
-1
1
2
3
4
5
6
-1
-2
-3
-4
-5
b) i- (0,4) ii- (-1,0), (4,0) iii- (1.5,6.25)
10
y
8
6
4
2
x
-2
-1
1
2
3
4
5
6
-2
-4
Parabola sheet
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7. a
b
10
10
y
y
8
8
6
6
4
4
2
2
x
x
-2
-1
1
2
3
4
5
6
7
-2
8
-1
1
-2
-2
-4
-4
c
2
3
4
5
6
d
10
3
y
8
2
6
1
y
x
4
-2
-1
2
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
-1
-2
1
-3
-2
-4
-4
-5
8. a) (3,9), (-1,1) b) (1,1) c) no intersection d) (6,14), (-1,0) e) (-2,-2), (2,-2)
9. a) 21 b) $837 c) $45 10. a) 30ᵒ C b) 5am c) 5ᵒ C 11. b) x = 10 c) 200m2
Parabola sheet
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4
5
6