ALGEBRA 1

UNIT 6

(9 LESSONS + 2 PRACTICE + 1 QUIZ + 1 STUDY GUIDE + 1 TEST = 14 DAYS)

Date Lesson Plan Standard(s) Other

M 1/27 STAFF DEVELOPMENT DAY

T 1/28 6-N1 Solve Quadratics by Inspection A.REI.4 Start Warm Ups & Hand Out HW Set #18

W 1/29 6-N2 Solve Quadratics by Inspection A.REI.4

Th 1/30 6-N3 Solve Quadratic Equations by Factoring, A.REI.4, A.SSE.3, Warm Up QuizFind Zeroes (Roots) A.APR.3

F 1/31 PRACTICE Start Warm Ups

M 2/3 QUIZ Collect HW Set #18

T 2/4 6-N4 Solve Quadratics by Completing the Square A.SSE.3 Hand Out HW Set #19 W 2/5 6-N5 Solve Quadratics by Completing the Square A.SSE.3 Warm Up Quiz

Th 2/6 6-N6 Solve Quadratics using Quadratic Formula A.REI.4 COMMON CORE WARM UP

F 2/7 6-N7 Solve Quadratics using Quadratic Formula, A.REI.4 COMMON CORE WARM UP Recognize Complex Solutions

M 2/10 6-N8 Choose the Best Solving Method COMMON CORE WARM UP

T 2/11 PRACTICE Start Warm Ups & Collect HW Set #19 & Hand Out HW Set #20

W 2/12 6-N9 Solve Equations by Factoring Completely A.REI.4, A.SSE.3, A.APR.3

Th 2/13 STUDY GUIDE Warm Up Quiz

F 2/14 TEST Collect HW Set #20

6 - N1Today, you will be able to:

“TOP FIFTEEN” TOPIC What is a QUADRATIC?

What are ROOTS or ZEROS?

What is a SOLUTION SET?

ANYTIME you solve a quadratic equation, you should get

_____ roots or zeros.

There are three methods we will learn to solve quadratic equations.

Today, the method we will use is _____________________!!!

Solve the following quadratic equations for all values of x. If necessary, write your answer in simplest radical form.

1. x2=121 2. x2=49

3. x2=144 4. x2=7

5. x2=11 6. x2=12

7. x2=200 8. x2=5

9. x2=17 10. x2=27

To use inspection, you must _________________________ the variable.

11. x2−8=28 12. 10 x2=90

13. 3 x2−9=0 14.

16

x2=216

15. 13−36 x2=−12

6 – N2Today, you will be able to:

“TOP FIFTEEN” TOPICSolve for all values of x. If necessary, write your answer in simplest radical form:

1. x2=10 ,000 2.

3. ( x−3 )2=1 4. ( x+4 )2=7

5. ( x+10 )2=5 6.

7. 3 ( x−2 )2=9 8. 2 ( x+2 )2−4=28

To find the zeros of an equation written in function notation,

REPLACE f(x) with ______________!

9. Find the zeros of .

10. The zeros of the function are

(1) -2 and 5 (3) -5 and 2

(2) -3 and 7 (4) -7 and 3

6 – N3Today, you will be able to:

“TOP FIFTEEN” TOPIC

Solve using Inspection.

However, there is another way to solve a quadratic called _____________!!

In order to use T-Bar, you must be able to __________________

using _________, __________, ______________, or _____________.

When you use T-Bar, your equation must be _________________________.

If (a ) (b )=0 , what can you conclude about a or b?

Solve using T-Bar.

Solve the following quadratic equations using T-Bar:

1. x2−9=0 2. x2+9 x−10=0

3. 6 x2−30 x=0 4. x2−7x+12=0

5. 2 x2−13 x−7=0 6. x2−4 x=12

7. x2=36 8. 3 x2+10 x=8

9. Find the zeros of

We cannot use T-Bar on this problem. Why not?

Then, how can we solve this problem?

UNIT 6 – PRACTICE #1

Solve the following quadratic equations using Inspection.

1. x2=529 2. x2=900

3. x2=19 4. x2=31

Solve the following quadratic equations using Inspection. Make sure all answers are in simplest radical form.

5. x2=48 6. x2=18

Solve the following quadratic equations using inspection.

7. 5 x2=45 8. 4 x2−10=90

9. ( x+7 )2=64 10. ( x−4 )2=3

Solve the following quadratic equations using T-Bar.

11. x2−196=0 12. x2+9 x+14=0

13. 10 x2−80 x=0 14. 2 x2−11 x+5=0

6 – N4Today, you will be able to:

“TOP FIFTEEN” TOPIC1. Solve x

2+8 x+12=0 using T-Bar.

Can we solve x2+8 x+12=0 using Inspection?

However, if we can rewrite x2+8 x+12 by

____________________________, then we can use Inspection!

Solve x2+8 x+12=0 using Inspection.

Find the zeros of the following quadratic equations using both T-Bar and Inspection:

2. f ( x )=x2+10 x+9T-Bar Inspection

3. f ( x )=x2−2 x−35T-Bar Inspection

Sometimes, when you are solving a quadratic equation, you will have a choice between using T-Bar and using Inspection.

However, which method MUST you use in the following problem?

4. Find the zeros of the function f ( x )=x2−4 x−2

6 – N5Today, you will be able to:

“TOP FIFTEEN” TOPICFind the zeros of each function:

1. f ( x )=x2+8 x+5 2. f ( x )=x2−6 x+4

3. f ( x )=x2−4 x−14 4. f ( x )=x2+6 x−11

5. 6.

7. Which equation has the same solution as x2−6 x−12=0 ?

(1) ( x+3 )2=21

(2) ( x−3 )2=21

(3) ( x+3 )2=3

(4) ( x−3 )2=3

6 – N6Today, you will be able to:

Standard Form of a Quadratic Equation:

Given the following quadratic equations, identify a, b, and c:

1. y=3 x2−5 x+8 a = ______ b = ______ c = ______

2. y=x2+4 x−9 a = ______ b = ______ c = ______

3.y=1

2x2+17

a = ______ b = ______ c = ______

4. y=−x2+x a = ______ b = ______ c = ______

So far, we have learned how to solve quadratic equations using

____________________ and _____________________.

There is one more way to solve a quadratic equation!

Today, we will learn how to use the _____________________________.

This formula will be provided to you on your reference sheet!

x=−b±√b2−4 ac2 a

Use the Quadratic Formula to solve the following equations. If necessary, round your answer to the nearest tenth .

1. 2 x2+5 x+3=0

2.

3. x2−3x=1

4. x2−4 x+5=0

6 – N7Today, you will be able to:

Use the Quadratic Formula to solve the following equations. Express your answers in simplest radical form.

1. 9 x2−5 x−1=0

2. x2−6 x+7=0

3. x2−10x+13=0

4. x2−8 x=24

5. 4 x2−12 x+7=0

6. How many real-number solutions does have?

(1) one (3) zero

(2) two (4) infinitely many

7. Is the solution to the quadratic equation written below rational or irrational? Justify your answer.

6 – N8Today, you will be able to:

Solve each quadratic equation using a method of your choosing – Inspection, T-Bar, Inspection by Completing the Square, or Quadratic Formula. Express all answers, if necessary, in simplest radical form.

Quadratic Formula:x=−b±√b2−4 ac

2 a

QUESTIONS TO CONSIDER:

Do I only have a squared term, with no “x” term at all? If yes, isolate the squared term and use INSPECTION!

Can I factor? If yes, use T-BAR!

Does my “x2” term have a coefficient of 1? If yes, use INSPECTION BY COMPLETING THE SQUARE!

Am I out of options? If yes, use QUADRATIC FORMULA!

1. x2−11x−26=0

2. x2=121

3. x2+4 x−3=0

4. 6 x2−24 x=0

5. 3 x2−8 x+4=0

6. 2 x2−8 x+3=0

7. 3 x2−10=65

8. x2−6 x−18=0

UNIT 6 – PRACTICE #2

Solve each quadratic equation using a method of your choosing - Inspection, T-Bar, Inspection by Completing the Square, or Quadratic Formula. Express all answers, if necessary, in simplest radical form.

Quadratic Formula:x=−b±√b2−4 ac

2 a

1. x2=49

2. x2+10 x+12=0

3. 5 x2+20 x=0

4. x2+7 x−18=0

5.

6. 2 x2−3 x+1=0

7. x2−4 x−4=0

8. 3 x2+x−5=0

6 – N9Today, you will be able to:

When solving, the _______________ of the polynomial tells you how many

___________ you will have!

Solve:

1. x4−13 x2+36=0 2. x3−81 x=0

3. d3−4 d2−21 d=0 4. 2 x2−98=0

5. 5 x2−20 x−60=0 6. y4−17 y2+16=0

7. 8 x2−50=0 8. 2 x3+12 x−10 x2=0

UNIT 6 – STUDY GUIDE

6-N1 through 6-N8

Solve the following equations. If necessary, write your answer in simplest radical form.

1. x2−81x=0 2. x2=19

3. x2+8 x+6=0 4. x2−8=10

5. 10 x2=810 6. x2−8 x=48

7. 3 x2+7 x−1=0 8. x2+12 x+28=0

9. Solve the following equation. Round answers to the nearest tenth.

10. Solve for all values of y:

11. Write an equation that defines h(x) as a trinomial where

h ( x )=(2− x ) (5 x+3 )+6 x2+4

Solve for x when h ( x )=0 .

12. When solving the equation by completing the square, which equation is a step in the process?

(1) (3)

(2) (4)

6-N9

13. Solve: x4−17 x2+16=0

14. The zeros of the function are

(1) (3)

(2) (4)

15. The zeros of the function are

(1) -1 and -2 (3) 1 and 2

(2) 1 and -2 (4) -1 and 2