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Unit 10B – Quadratics - Chapter 9 Name:
The calendar and all assignments are subject to change. Students will be notified of any changes
during class, so it is their responsibility to pay attention and make any necessary changes.
All assignments are due the following class period unless indicated otherwise.
Monday Tuesday Wednesday Thursday Friday
4
MapTesting
5
Section 9.1
Prop of Radicals
6
Section 9. 1b
Properties of
Radicals
7
Section 9.3
8
Quick Quiz
Section 9.4 Completing
the Square
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Section 9.4b
12
Section9.4c/ 9.5a
Quadratic Formula
13
Section 9.5 b
14
9.5c
15
Review Quadratics
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Review Quadratics
19
Test on Solving
Quadratics
Section Page Assignment
9.1 p. 485
9.1b p. 486
9.3 p. 501
9.4 p. 511
9.4b
9.5a p. 521
9.5b
Chapter 9 Review
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Lesson 9.1 – Properties of Radicals Algebra 1
Essential Question How can you multiply and divide square roots?
For each operation with square roots, compare the results obtained using the two indicated orders of
operations. What can you conclude?
a. Square Roots and Multiplication
Is 4 9 equal to 4 9?
In general, is a b equal to ?a b Explain your reasoning.
b. Square Roots and Division
Is 100
4equal to
100
4
In general, is a
bequal to ?
a
b Explain your reasoning.
Core Concepts
Product Property of Square Roots
Words The square root of a product equals the product of the square roots of the
factors.
Numbers 9 • 5 9 • 5 3 5
Algebra • , where , 0ab a b a b
1. Simplifying Radicals with the Product Property
Simplify each radical into its simplest form.
(a) (b) (c) (d) (e)
(f) (g)
50 125 48 300 72
128 288
1 EXPLORATION: Operations with Square Roots
3
Quotient Property of Square Roots
Words The square root of a quotient equals the quotient of the square roots of the
numerator and denominator.
Numbers 3 3 3
4 24 Algebra , where 0 and 0
a aa b
b b
2. Simplifying Radicals with the Quotient Property
Simplify each radical into its simplest form.
(a) (b) (c) (d) (e)
3. Simplify each radical into its simplest form.
(a)
6162g (b) 7512h (c) 4
196
r (d)
3
2
49
64
x
y
Lesson 9.1 – Properties of Radicals – Day 2 Algebra 1
A radical is simplest form when 3 conditions are met:
No radicands have…
No radicands contain…
No radicals appear in the…
9
25
25
18
6
72
90
40
50
32
4
1. Dividing Radicals (Rationalizing the Denominator) Simplify the Radical
(a) (b) (c)
(d) (e) ba
b
(f) 22
42
Practice Dividing Radicals
2. 7
4 3.
5
5 4.
2
10 5.
48
3
6. 75
9
7.
210
6
8.
37
12
2
5
14
7
35
6
23
4
5
Lesson 9.1 Worksheet Name _____________________________
I. Simplify each expression completely.
1. √ 2. √ 3. √
4. √ 5. √ √ 6.
√
7. √
8. √
9. 7√
10. √
11. √
12.
√
13. √
√ 14. √
15.
√
√
6
Lesson 9.3 – Solving Quadratic Equations Using Square Roots Algebra 1
Essential Question How can you determine the number of solutions of a quadratic
equation of the form ax2 + c = 0?
1. Finding Square Roots Evaluate.
(a) (b) (c) (d)
2. What is the square root of 36?
3. Solving Quadratics Equations in the Form:
Solve the following quadratic equations.
(a) (b) (c)
4. Solving Quadratics Equations in the Form:
Solve the following quadratic equations.
(a) (b) (c)
(d) ( e) 2
2 196x (f) 2
2 7 49x
81 100 64 9
cx 2
812 x 172 x 52 x
02 cax
01222 x 012 x 0273 2 x
06012 2 x
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5. Application Exercise – Falling Object Model
You have entered Mr. Esbrook’s first annual “egg dropping
contest”. The goal is to create a container for an egg so it can be
dropped from a height of 32 feet without breaking the egg. In you
quest to become egg-dropping champion, you have asked your
Algebra class to determine the time it will take for the egg
container to hit the ground. About how long will it take for the
egg’s container to hit the ground? Assume there is no air
Algebra: Section 9.1/ 9.3 Worksheet
Name______________________________________________Date____________________Hour______
Solve each equation using square roots. Simplify square roots if necessary. There should be no decimal answers.
1. x2 = 100 2. 2y2 = 32 3. ¼ a2 = -6
4. 10 – 2x2= 4 5. 7y2 + 14 = 0 6. 3b2 – 6 = 9
7. ½ x2 – 7 = 1 8. 2x2 + 5 = 9 9. -4x2 + 6 = -394
10. 6 – 3x2 = 27 11. 2
81 3 1 49x 12. 2
16 3 25x
8
simplify.
√ 13. √ 14. √
15. √
16. √
17. -3√
18. -5 √
√ 19. Find the area of a square with side length √
20. Find the area of a triangle with height √ and base √ .
21. Using the Falling Object Model found in section 9.1. Determine approximately how long it will take a I-
phone to hit the ground when dropped from a window 25 feet above the ground.
Lesson 9.4(a) – Completing the Square (w/ Leading Coefficient 1) Algebra 1
1. Completing the Square Complete the square so that each expression is a perfect square trinomial. Then factor the trinomial.
(a) (b) (c)
xx 122 xx 82 xx 302
Completing the Square To complete the square for any quadratic
expression in the form
add ____________ of the second coefficient (b)
_____________ to the end.
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2. Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square.
(a) (b)
(c) (d)
Lesson 12.4(b) – Completing the Square (w/ Leading Coefficient 1) Algebra 1
Warm-Up Exercise Solve by Completing the Square.
(a) (b) Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square.
1. 2.
24102 xx 07262 xx
0422 xx 032
12 xx
01422 xx 7142 xx
41082 2 xx 0848 2 xx
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3. 4. 210 13 9 0x x
5. 23 6 1 0x x 6.
212 8 2 0x x
In Exercises 7-12, determine whether the quadratic function has a maximum or minimum value.
Then find the value.
7. 2 4 3y x x 8. 2 6 10y x x 9. 2 8 2y x x
10. 2 10 8y x x 11. 23 3 1y x x 12. 24 8 12y x x
0263 2 xx
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13. Choosing a Method to Solve a Quadratic Determine the easiest method to solve the quadratics below. Tell which method you used, and then solve the equation.
(a) (b)
(c)
Lesson 9.5(a) –The Quadratic Formula Algebra 1
Essential Question How can you derive a formula that can be used to write the
solutions of any quadratic equation in standard form?
The following steps show a method of solving 2 0.ax bx c Explain what was done in each step.
2
2 2
2 2 2 2
2 2 2 2
2 2
0 1.
4 4 4 0 2. _____________________________
4 4 4 3. _____________________________
4 4 4 4. _____________________________
2 4 5.
ax bx c
a x abx ac
a x abx ac b b
a x abx b b ac
ax b b ac
Write the equation.
2
2
2
_____________________________
2 4 6. _____________________________
2 4 7. _____________________________
4 8. _____________________________
2
ax b b ac
ax b b ac
b b acx
a
:Quadratic Formula
0405 2 x 0652 xx
52582 2 xx
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Core Concepts
Quadratic Formula
The real solutions of the quadratic equation2 0 ax bx c are
2 4
2
b b acx
a
Quadratic Formula
where 0a and 2 4 0. b ac
Interpreting the Discriminant
2 4 0b ac 2 4 0b ac 2 4 0b ac
Methods for Solving Quadratic Equations
Practice
In Exercises 1–6, solve the equation using the Quadratic Formula.
1. 2 10 16 0x x 2. 2 2 8 0x x 3. 23 2 0x x
Method Advantages Disadvantages
Factoring
(Lessons 7.5–7.8)
Graphing
(Lesson 9.2)
Using Square Roots
(Lesson 9.3)
Completing the Square
(Lesson 9.4)
Quadratic Formula
(Lesson 9.5)
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4. 2 6 13x x 5. 23 5 1 7x x 6. 24 8 12 6x x
7. A square pool has a side length of x feet. A uniform border around the pool is 1 foot wide. The total area of
the pool and the border is 361 square feet. What is the area of the pool?
In Exercises 8–10, determine the number of real solutions of the equation.
8. 2 6 3 0x x 9. 2 6 9 0x x 10. 2 3 8 0x x
In Exercises 11–13 find the number of x-intercepts of the graph of the function.
11. 2 4 3y x x 12. 2 14 49y x x 13. 2 8 18y x x
In Exercises 14–16, solve the equation using any method. Explain your choice of method.
14. 2 4 4 16x x 15. 2 8 7 0x x 16. 23 5 0x x
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Lesson 9.5(b) Worksheet – The Quadratic Formula Name
1. Recite the Quadratic Formula.
x =
Solve each quadratic equation by using the Quadratic Formula.
You must solve by using the Quadratic Formula. No other method will be accepted.
2. 01452 xx 3. 018112 xx 4. 022 xx
5. 0822 xx 6. 0132 2 xx 7. 0372 2 xx
8. 0302 xx 9. xx 23 2 10. 0633 2 xx
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11. 3145 2 xx 12. 4113 2 xx 13. 8103 2 xx
14. 042 2 xx 15. 5102 2 xx
Lesson 9.4-9.5 Review Worksheet Name_______________________________________ Algebra 1
I. Using the Discriminant
Find the discriminant of each quadratic equation and give the number and type of the solutions of the equation.
1. 01152 xx 2. 0752 xx 3. xx 10252
4. 2256 xx 5. 0512 2 x
II. Solving Quadratic Equations by Using the Quadratic Formula
Use the Quadratic Formula to solve each of the quadratic equations below. Be sure to simplify your solutions.
6. 18150 2 xx 7. 2457 xx 8. 0467 2 xx
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9. 0142 xx 10. 0458 2 xx 11. xx 836 2
III. Solving Quadratic Equations by Completing the Square
Solve each of the quadratic equations below by Completing the Square. Be sure to simplify your solutions.
12. 03242 xx 13. 028162 2 xx 14. 66303 2 xx
IV. Solving Quadratic Equations by Choosing a Method
Solve each of the quadratic equations below by any method
(Complete the Square, Factoring, Square Roots, or Quadratic Formula)
15. 1482 xx 16. xx 924 2 17. 136 2 xx
18. 02452 xx 19. 1211219 2 x 20. 01054 2 x
