Thursday, October 11, 2012
Test-ForSiauliaiStudents-Quadratic_Functions-TeacherJim.nb
End-of-Cooperation
Test
Topic: Quadratic Functions
Class: Siauliai and Aydin
Date: March 27th, 2012
Name:
(1) Matching Graphs and Functions (8P)
Open Close
1.
Which curve belongs to x2 3, which one is 4
Write an answer.
(2P)
x2 ?
y
6
4
2
3
2
1
1
2
3
x
2
4
2.
Which curve is the graph of x
Write an answer.
(2P)
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3 2 and which one is the graph of x
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4 2?
1
Thursday, October 11, 2012
Test-ForSiauliaiStudents-Quadratic_Functions-TeacherJim.nb
200
150
100
50
10
3.
5
5
10
x
What is the vertex of the green function?
What is the vertex of the red function?
Write an answer.
(2P)
y
100
80
60
40
20
40
4.
30
Which curve is the graph of - x
x 1 2 3?
Write an answer.
(2P)
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20
10
x
5 2 + 6 and which one is the graph of
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2
Thursday, October 11, 2012
Test-ForSiauliaiStudents-Quadratic_Functions-TeacherJim.nb
y
20
4
2
2
4
x
20
40
60
80
(2) Graphing Quadratic Functions and
Solving Quadratic Equations (16P)
Open Close
5.
x2
a)
(2P)
Define the function f x
7x
9 and plot it on the interval [-1,8].
b)
Measure, by cursor measurement, the coordinates of the vertex.
Write an answer.
(1P)
c)
Find, not using cursor measurement, and correct to three places of
decimals, the x-intercepts.
Find also the y-intercept.
Write an answer.
(2P)
d)
On the graph of f[x] indicate the x-intercepts with green points and the yintercept with a blue point.
(2P)
a)
Define the quadratic function f that passes through the three points (0,4),
(2,3) and (5,6).
Write down the functional form of f.
(2P)
6.
b)
Plot the function f along with the three points listed above.
c)
What is the equation of the axis of symmetry of f?
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(2P)
(1P)
3
a)
Solve the equation x2 - x - 1 = 0.
Write your answers as decimals.
b)
Verify each solution.
7.
(2P)
(2P)
(3) Applications (16P)
Open Close
The height (in metres) of an experimental rocket, launched upright into the air,
without considering air resistance, is:
f[x] = -9.81 x2 + 100 x, where x is the time since launch, in seconds.
8.
(a) What is the maximum height (to one decimal place) the rocket reaches? (2P)
(b) How many seconds (to the nearest unit) after the launch does the rocket reach
its maximum height? (1P)
(c) How many seconds after the launch does the rocket hit the ground? (1P)
Write an answer for each part.
Based on data from past years, the annual profit of a company selling artisan
9.
Thursday, October 11, 2012
Test-ForSiauliaiStudents-Quadratic_Functions-TeacherJim.nb
Imagine a Norman window is to have a perimeter of 5 metres.
x represents the width of the rectangular part of the window while y represents the
height of the rectangular part.
(a) Define the function f[x] for the area of the entire Norman window.
Write an answer.
Hint: 5 = 2y + x + (
(2P)
x
)
2
(b) Plot the function.
Label the x-axis "x (m)" and the y-axis "Area (m2 )". (3P)
(c) Find the maximum area that the window can have.
Write an answer.
(2P)
(d) What would the area of the window be if planning restrictions meant that the
width x could not be more than 1.1 metres?
Write an answer.
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(1P)
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5