intensive math algebra i

Day 17

Student Packet

Summer 2013

Simplifying Radical Expressions

Intensive Math-Algebra I Mini-Lesson MA.912.A.7.1 and MA.912.A.6.2

Graphing Quadratic Equations

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Summer 2013 Intensive Mathematics – Algebra 1 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


Example # 1: Textbook page 535


Guided Practice: Textbook page 544: 14 - 19


Guided Practice: Textbook page 545: 26 - 27

Additional Practice

1. Select the equation that represents the graph.

A. 𝑦 = 𝑥 2− 2

B. 𝑦 = 2𝑥 + 2

C. 𝑦 = (𝑥 − 2) 2

D. 𝑦 = 𝑥 2

2. Which equation is graphed below?

A. 𝑦 = −2 𝑥 2− 2

B. 𝑦 = 𝑥 2+ 2

C. 𝑦 = −2 𝑥 2+ 2

D. 𝑦 = 𝑥 2− 2


3. Graph = 2− + Find the axis of symmetry and the vertex.

A.

The axis of symmetry is x = 0. The vertex is (0, 4).

B.

The axis of symmetry is x = 4. The vertex is (4, 0).

C.

The axis of symmetry is =

2.

The vertex is (

2

)

D.

The axis of symmetry is = −

2.

The vertex is (−

2

)

4. Which of the following is the graph of = 2− − ?

A.

B.

C.

D.


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.




Guided Practice: Textbook page 604: 10 - 32 (even numbers)



Guided Practice: Textbook page 604: 36 – 46 (even numbers)


Guided Practice: Textbook page 610: 10 – 20 (even numbers)

Small Group Practice: Focus MA912A62

Mini-Assessment MA912A62 Score: ____________

Home Learning: HL MA912A62


Focus Practice MA912A72

1. Which of the following is the graph of the function ?

A.

B.

C.

D.


2. Which of the following equations represents the graph shown below?

A.

B.

C.

D. –



A.

B

C. y =

D


A.

B.

C.

D.



A.

B.

C.

D.



A. B. C.

D. –


A. B. C.

D. –


A.

B.

C.

D.



A.

B.

C.

D.


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. 144 feet

B. 288 feet

C. 240 feet

D. 432 feet


4. Which quadratic equation best represents the parabola shown below?

A.

B.

C.

D.

5. Which is the graph of ?

A.

B.

C.

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. 16 sec

B. 64 sec

C. 4 sec

D. 8 sec


7. Which best represents the graph of ?

A.

B.

C.

8. Which quadratic equation best represents the parabola shown below?

A.

B.

C.

D.


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. at t = 0.5625 seconds and t = 1 second

B. at t = 0.5625 seconds only

C. at t = 1 second only

D. the ball will never reach a height of 9 feet

11. Which graph represents the quadratic function ?

A.

B.

C.

D.


Focus Practice MA.912.A.6.2

1. Simplify the radical expressions below:

a) √

√ √

b) √ √

c) √ √

d) √ √

e) √ √

√

f) √ √

g) √ √ √

h) √

√ √

i) √ √

2. What is the value of x in the equation shown below?

√

√ √


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.


a.

b.

c.

d.

4. The expression is equivalent to

a.

b. c. 8 d. 4


a.

b.

c.

d.



a.

b.

c.

d.

7. When is written in simplest radical form, the result is . What is the value of k? a. 20 b. 10 c. 7 d. 4

8. Expressed in simplest radical form, the product of is

a.

b.

c.

d.


a.

b. c. 8

d. 4


a.

b.

c.

d.

11. Simplify:

12. Express in simplest radical form.

intensive math algebra i

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