MPM 2D0
Solving Quadratic Equations Assignment
Name:
Review of 4 Methods of Solving Quadratic Equations
1. Solve by Graphing the Corresponding Quadratic Function. Show all work and include a clearly
labelled graph.
a)
𝑥 2 = 4𝑥 − 4
b) 2𝑥 2 − 5𝑥 − 12 = 0
2. Solve the following quadratic equations by Factoring.
a)
4𝑥 2 − 3𝑥 = 9
b) 16𝑥 2 = 25
c)
−5𝑥 = −𝑥 2 − 6
d)
3𝑥 2
4
+
5𝑥
4
1
2
− =0
3. Solve the following quadratic equations by completing the square.
a) −4𝑥 + 𝑥 2 − 2 = 0
b) 3𝑥 2 − 2𝑥 − 6 = 0
4. Solve the following quadratic equations by using the quadratic formula. Write the solutions as
approximate solutions to the nearest hundredth.
a)
𝑥 2 + 3𝑥 + 1 = 0
b) 4𝑚2 − 𝑚 − 11 = 0
c) 30𝑥 2 − 17𝑥 − 450 = 0
5. Solve each of the following equations using the most appropriate method.
a) 𝑥 2 − 3𝑥 = 0
c)
b) 36𝑥 2 − 49 = 0
2𝑥 2 + 3𝑥 − 7 = 0
d)
𝑥2
4
𝑥
1
−3+9=0
Answers
3
1. a) x = 2, 2 b) x = 4, − 2
3. a) 𝑥 = 2 ± √6
5. a) 0, 3 b)
7
6
b) 𝑥 =
7
,−6
c)
3
5
5
2. a) 𝑥 = 4 , 0 b) 𝑥 = 4 , − 4
1±√19
3
−3±√65
4
4. a) -0.38, -2.68
d)
2
3
2
,3
c) 2, 3
1
d) 𝑥 = 3 , −2
b) 1.79, -1.54 c) 4.17, -3.60
Assignment
Solving Quadratic Equations
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1110371
Level 4
Level 3
Level 2
Level 1
Below Level 1
Know ledge and U
80 - 100%
70 - 80%
60 -70%
50 - 60%
Solving Quadratic
0
Level 4
80 - 100%
Knowledge
and
Understanding
Solving
Quadratic
Equations using
4 methods.
Demonstrates
complete
understanding
of the
mathematical
concepts used
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to solve the
Demonstrates co problem(s);
logic is
mathematically
sound.
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Demonstrates su
Level 3
70 - 80%
Level 2
60 -70%
Level 1
50 - 60%
Below Level 1
Demonstrates
substantial
understanding
of the
mathematical
concepts used
to solve the
problem(s);
logic is
mathematically
sound.
Demonstrates
some
understanding
of the
mathematical
concepts needed
to solve the
problem(s);logic
contains some
errors.
Demonstrates
very limited
understanding
of the
underlying
concepts needed
to solve the
problem(s) ;
logic is faulty or
not included.
Demonstrates
insufficient
understanding
of the concepts
needed to solve
the
problem(s)or
nothing is
included
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Demonstrates ve
Demonstrates ins
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Thinking
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Demonstrates so
0
Thinking
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Explanation is
Explanation is tho thorough,
detailed, and
understandable;
frequent use of
math
terminology and
notation.
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Explanation is
minimal yet
understandable
and includes
some detail;
some use of
math
terminology and
notation.
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Explanation is
limited with little
or no detail and
is difficult to
understand;
infrequent or no
use of math
terminology and
notation.
Explanation is
difficult to
understand and
contains little or
no detail; no
use of math
terminology and
notation.
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Explanation is min
Little
explanation is
given and
solution
contains little or
no detail; no
use of math
terminology and
notation.
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Little explanation
Explanation is limi
Explanation is diff
Completion
0
Completion
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All components
All components a and steps are
included and
correct.
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All or most
components and
steps are
included and
mostly correct.
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All or most compo
Some
components and
steps are
included and
somewhat
correct.
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Some component
Very few
components and
steps are
included and
somewhat or
not correct.
Insufficient
components and
steps are
included and/or
not correct.
1110375
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Communication
Very few compo
Insufficient comp
Format and Prese
0
Communicatio
n
Format and
Presentation
Work is
presented in a
very clear and
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organized
Work is presente manner that is
easy to follow.
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Work is
presented in a
clear and
organized
manner that is
mostly easy to
follow.
Work is
presented in a
somewhat clear
and organized
manner but may
be hard to
follow.
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Work is presente
Work is unclear, u
Work is unclear,
unorganized,
and hard to
follow.
Graphs are
accurate and
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neatly drawn.
Graphs are accu All details are
clearly labelled
and justified.
Graphs are fairly
accurate and
neatly drawn.
Most details are
clearly labelled
and justified.
Graphs are
drawn with
some accuracy.
Some details
are labelled and
justified.
1110388
4263653
Communication
Very little w ork is
Graph
0
Work is presente
Communicatio
n
Graph
Very little work
is shown.
Graphs are
drawn with little
accuracy. Few
details are
labelled and
justified.
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Graphs are fairly
Graphs are draw
Graphs are draw
Graphs are not d
Graphs are not
drawn or are
incomplete.