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Intensive Math-Algebra I
Mini-Lesson MA.912.A.7.1 and MA.912.A.6.2
Graphing Quadratic Equations
Simplifying Radical Expressions
Student Packet
Summer 2013
Day 17
Name: _____________________________________________________ Date: __________________
Part I: Benchmark MA.912.A.7.1
Graph quadratic equations with and without graphing technology.
This benchmark will be assessed using MC items.
Students will:
• Identify the graph of a quadratic function given its equation.
• Use the graph of a quadratic function to solve a real-world problem.
Content Limits
• In items set in a real-world context, the quadratic equation should be presented. The context of the
problem should require the student to interpret which value will be the solution.
• Items must use quadratic equations with integral coefficients except for items set in a real-world
context.
• Items whose roots would be nonintegral should have the vertex and at least two other points labeled.
• Quadratic equations will be presented in standard form only.
• Graphics should be used in all of these items.
Lesson MA.912.A.7.1
Textbook: Prentice Hall Algebra 1
I can …
• Identify the graph of a quadratic function given its equation.
• Use the graph of a quadratic function to solve a real-world problem.
Vocabulary
• Quadratic Function
• Standard Form of a Quadratic Function
• Parabola
• Axis of Symmetry
• Vertex
• Minimum
• Maximum
Essential Understanding
• A quadratic function is a type of nonlinear function that models certain situations where the rate of
change is not constant.
•
The graph of a quadratic function is a symmetric curve with a higher or lowest point corresponding to a
maximum or minimum value.
•
The graph of a quadratic function is called parabola
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Example # 1: Textbook page 535
Example # 2: Textbook page 542
Guided Practice: Textbook page 544: 14 - 19
Example # 3: Textbook page 542
Guided Practice: Textbook page 545: 26 - 27
Additional Practice
1. Select the equation that represents the graph.
2
A. 𝑦 = 𝑥 − 2
B. 𝑦 = 2𝑥 + 2
C. 𝑦 = (𝑥 − 2)
D. 𝑦 = 𝑥
2
2
2. Which equation is graphed below?
2
A. 𝑦 = −2 𝑥 − 2
2
B. 𝑦 = 𝑥 + 2
2
C. 𝑦 = −2 𝑥 + 2
2
D. 𝑦 = 𝑥 − 2
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
3. Graph
=
2
−
+
Find the axis of symmetry and the vertex.
A.
B.
The axis of symmetry is x = 0.
The vertex is (0, 4).
The axis of symmetry is x = 4.
The vertex is (4, 0).
C.
D.
The axis of symmetry is
The vertex is (2
=
.
The axis of symmetry is
2
)
4. Which of the following is the graph of
The vertex is (− 2
=
2
−
)
− ?
A.
B.
C.
D.
Summer 2013
= − 2.
Intensive Mathematics – Algebra 1
Day 17
Small Group Practice: Focus MA912A71
Mini-Assessment MA912A71
Score: ____________
Home Learning: HL MA912A71
Part II: Benchmark MA.912.A.6.2
Add, subtract, multiply, and divide radical expressions (square roots and higher).
Also assesses MA.912.A.6.1 Simplify radical expressions.
This benchmark will be assessed using MC items.
Students will:
• Add, subtract, multiply, and/or divide radical expressions and simplify the results.
Content Limits
• Items will assess square roots only.
• Radicands with variables will contain positive integral exponents.
• Items with variables must state restrictions to the domain.
Stimulus Attribute
• Items should be set in a mathematical context.
Response Attribute
•
Multiple-choice options must be presented with rationalized denominators.
Lesson MA.912.A.6.2
Textbook: Prentice Hall Algebra 1
I can …
• Simplify radical expressions
Vocabulary
• Radical Expressions
• Rationalize the denominator
Essential Understanding
• A radical expression is an expression that contains a radical (√)
•
A radical expression is simplified if the following statements are true:
o The radicand has no perfect-square factors other than 1
o The radicand contains no fractions
o No radicals appear in the denominator of the fraction.
•
You can simplify radical expressions using multiplication and division properties of square roots.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Example # 1: Textbook page 600
Example # 2: Textbook page 601
Guided Practice: Textbook page 604: 10 - 32 (even numbers)
Example # 3: Textbook page 603
Example # 4: Textbook page 603
Guided Practice: Textbook page 604: 36 – 46 (even numbers)
Example # 5: Textbook page 607
Guided Practice: Textbook page 610: 10 – 20 (even numbers)
Small Group Practice: Focus MA912A62
Mini-Assessment MA912A62
Score: ____________
Home Learning: HL MA912A62
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Focus Practice MA912A72
1. Which of the following is the graph of the function
?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
2. Which of the following equations represents the graph shown below?
A.
B.
C.
D.
Summer 2013
–
Intensive Mathematics – Algebra 1
Day 17
3. Which of the following equations represents the graph shown below?
A.
B
C. y =
D
4. Which of the following equations represents the graph shown below?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
5. Which of the following is the graph of the function
?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
6. Which of the following is the graph of the function
?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
7. Which of the following equations represents the graph shown below?
A.
B.
C.
D.
–
8. Which of the following equations represents the graph shown below?
A.
B.
C.
D.
–
9. Which of the following equations represents the graph shown below?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
10. Which of the following is the graph of the function
?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Home Learning
MA.912.A.7.1: Graphing Quadratic Equations
1.
Which equation is graphed below?
A.
B.
C.
D.
2. Which is the graph of the quadratic equation
?
A.
B.
C.
D.
3. The height in feet of a rocket launched from the ground can be modeled by the function
where x is the time in seconds after it is launched. What is the rocket’s maximum height?
A.
B.
C.
D.
144 feet
288 feet
240 feet
432 feet
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
4. Which quadratic equation best represents the parabola shown below?
A.
B.
C.
D.
5. Which is the graph of
A.
C.
?
B.
D.
6. A golfer hits the golf ball. The quadratic function
gives the time x seconds after the golf
ball is at height 0 feet. How long does it take for the golf ball to return to the ground?
A.
B.
C.
D.
16 sec
64 sec
4 sec
8 sec
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
7. Which best represents the graph of
?
A.
B.
C.
8. Which quadratic equation best represents the parabola shown below?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
9. Which of the following quadratic equations best represents this graph?
A.
B.
C.
D.
10. The equation
models the height of a soccer ball t seconds after it is kicked. Approximately when
will the ball reach a height of 9 feet?
A.
B.
C.
D.
at t = 0.5625 seconds and t = 1 second
at t = 0.5625 seconds only
at t = 1 second only
the ball will never reach a height of 9 feet
11. Which graph represents the quadratic function
?
A.
B.
C.
D.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Focus Practice MA.912.A.6.2
1. Simplify the radical expressions below:
a) √
√
√
√
b) √
√
√
d) √
√
c)
e)
f)
√
√
√
g) √
h)
i)
√
√
√
√
√
√
√
√
√
2. What is the value of x in the equation shown below?
√
√
√
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
Home Learning
MA.912.A.6.2: Simplifying Radical Expressions
1. What is
expressed in simplest radical form?
a.
b.
c.
d.
2. The sum of
and
is
a. 15
b. 18
c.
d.
3. What is
expressed in simplest radical form?
a.
b.
c.
d.
4. The expression
is equivalent to
a.
b.
c. 8
d. 4
5. The expression
is equivalent to
a.
b.
c.
d.
Summer 2013
Intensive Mathematics – Algebra 1
Day 17
6. What is
expressed in simplest radical form?
a.
b.
c.
d.
7. When
a.
b.
c.
d.
is written in simplest radical form, the result is
. What is the value of k?
20
10
7
4
8. Expressed in simplest radical form, the product of
is
a.
b.
c.
d.
9. The expression
is equivalent to
a.
b.
c. 8
d. 4
10. What is
expressed in simplest radical form?
a.
b.
c.
d.
11. Simplify:
12. Express
Summer 2013
in simplest radical form.
Intensive Mathematics – Algebra 1
Day 17