Tuesday March 17, 2020 Activator · What is the “Box Method?” It is a way to multiply with...

Tuesday March 17, 2020 Activator

What is the “Box Method?” It is a way to multiply with variables, an easier way to distribute.

Multiply (74)(392) = 29008

Multiply (70+4)(300+90+2) = 29008

Can you expand integers (normal numbers)? Yes

Why is the method used? to double distribute

Page #3Lesson 7.1

Today’s New Vocab (1 of 4)

+ 21,000 + 6,300 + 140

+ 1,200 + 360 +8

70+4

300 +90 +2Multiply using the “Box Method”

There must be a

sign in every box.Write down all of the boxes.

21,000 + 6,300 + 140 + 1,200 + 360 + 8 is 29,008

Combine like terms

Page #3Lesson 7.1

(2 of 4)

Combine Like Terms (CLT)

Definition

Example(s) Non-Example(s)

FactsTo write the answer

in an easier way.

• Used only with Add and Subtract

• The exponent does NOT change.

4𝑥2 + 3𝑥2 = 7𝑥2

4𝑥2 − 3𝑥2 = 𝑥24𝑥2 + 3𝑥3 ≠ 7𝑥5

Not the same exponent

Today’s New Vocab (3 of 4)Combine Like Terms: Does the exponent change?

Addition vs. No why? The exponent is multiplication.

(𝑥3) + (𝑥3) = 2𝑥3Subtraction

Exponent change? No

(5𝑥3) − (𝑥3) = 4𝑥3

Exponent change? No

𝑥3 + 𝑥3 = 2𝑥3 5𝑥3 − 𝑥3 = 4𝑥3

Why? We did not multiply a variable by a variable.

Today’s New Vocab (4 of 4)Combine Like Terms Will the answer have an equal sign? No Why? No equal sign in the question.

Line 1: (7𝑥3+ 3𝑥2) - (9x - 5𝑥2)

Line 2: 7𝑥3+ 3𝑥2 - 9x + 5𝑥2

Line 4: 7𝑥3 + 8𝑥2 - 9x

Distribute

Combine Like Terms

Line 3: 7𝑥3+ 3𝑥2 + 5𝑥2 - 9x Commute

Page #4Lesson 7.1

Tuesday March 17, 2020 Work Period

(2𝑥2 + 6x + 5 ) - (6𝑥2 +3x + 5)

If A=(2𝑥2 + 6x + 5 ) and B=(6𝑥2 +3x + 5), what is A-B?

2𝑥2 + 6x + 5 - 6𝑥2 - 3x - 52𝑥2- 6𝑥2 + 6x - 3x + 5 - 5

-4𝑥2 + 3x + 0

-4𝑥2 + 3x

Distribute

Commutative

Combine like Terms

Page #4Lesson 7.1

.

Tuesday March 17, 2020 Exit TicketWhat is the sum of 8𝑥2 - x + 4 and x - 5 ?

(8𝑥2 - x + 4) + (x – 5) 8𝑥2 - x + 4 + x - 5

8𝑥2 + 0x - 1 8𝑥2 - 1

8𝑥2 - x + x + 4 - 5

Distribute

Commutative

Combine like Terms

Page #4 Lesson 7.1

Today’s Objective

Students will be able to use the box method and combine like terms.

Unit 7Lesson 1

Wednesday April 10, 2020 Activator

Monomial

2𝑥3(5𝑥3) 2𝑥3 + 5𝑥3

Simplify the expressionsMonomial Monomial Monomial

10𝑥6

7𝑥32∙ 𝑥3(5)(𝑥3)

2∙ 5 𝑥3(𝑥3) Does the exponent change?No Why? Addition and subtraction

does not change exponents.

Page #7Lesson 7.2

(1 of 4)

Monomial

Definition


Facts

• has one sign and/or number

and/or variable

-1 -1𝑥2

3x 5 8𝑥4

x - 1 2x+4

−2𝑥2 + 3𝑥

Is one part of an expression

Page #7Lesson 7.2

Today’s New Vocab (2 of 4)Simplify the expression

x (x – 4)

x

x – 4

Can this be graphed? NoWhy? The variable needs distributed.

𝑥2 - 4x

A sign (±) 𝑚𝑢𝑠𝑡 𝑔𝑜 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑏𝑜𝑥.

Are these like terms? ______Same variable & same exponent

No+ 𝒙𝟐

- 4x

Page #7Lesson 7.2


x (𝑥2 + x - 4) Write all boxes down


Are these like terms? ______Same variable & same exponent

+𝒙𝟑 +𝒙𝟐 -4xx

𝑥2 + x - 4

𝑥3 + 𝑥2 - 4x

No Can this be graphed? NoWhy? The variable needs distributed.


(x + 3)(x - 4) Write all boxes down


+𝒙𝟐 -4x

+3x -12

x + 3

x -4 𝑥2 − 4𝑥 + 3𝑥 − 12

𝑥2 − 1𝑥 − 12Can this be graphed? YesWhy? The variables are in ( ).

Page #8Lesson 7.2

Wednesday April 10, 2020 Work Period

.

The expression (𝑥 − 6)2 is equivalent to

+ 𝒙𝟐 - 6x

- 6x + 36

𝑥 − 6𝑥

−6

Write all boxes down

𝑥2 − 6𝑥 − 6𝑥 + 36

𝑥2 − 12𝑥 + 36

LikeTerms

Page #8Lesson 7.2

Wednesday April 10, 2020 Exit Ticket F(x) = (𝑥 − 6)2

x G(x)

4 4

5 1

6 0

7 1

G(x) = 𝑥2 − 12𝑥 + 36 𝑎𝑛𝑑

Does G(x) and F(x) have an infinite (ALL) number of solutions?

Yes, because it is the same line.

Today’s Objective

Students will be able to multiply polynomials.

Unit 7Lesson 2

Friday April 12, 2020 Activator Simplify the following expressions. Are they equivalent? YES

x(x) -2𝑥2 + 3𝑥2

𝑥2 𝑥2Does the exponent change? Does the exponent change?

Yes. Why? Multiplying variables

No Why? Combining variables

Page #11Lesson 7.3

Today’s New Vocab (1 of 4)Axis of Symmetry –

x = lines that splits the graph in half.

Root, Zero, or Solutions –

Where the graph crosses the x-axis.

Vertex – The maximum or Minimum point on the graph.

Page #11Lesson 7.3

.

When x = -1 and x = 3, write the factors

(x + 1) ( x - 3) = 0 (x + 1) = 0 ( x - 3) = 0

x = -1 x = 3 +1 +1 -3 -3

Solution

Factor x - 3 = 0 x + 1 = 0

Factor

Solution


To write the factors, you need to sign switch from the solutions.

Page #11Lesson 7.3


+ 𝒙𝟐 - 3x

+ 1x -3

Determine the product of the following expression.

𝑥 − 3𝑥

+1


𝑥2 + 1𝑥 − 3𝑥 − 3

𝑥2 − 2𝑥 − 3

LikeTerms

(x + 1)(x - 3)

Page #11Lesson 7.3

Today’s New Vocab (4 of 4)Graph the polynomial f(x) = (x + 1)(x − 3)

x f(x)

-1 0

0 -3

1 -4

2 -3

3 0

BOX the Roots’s

X = _____X = _____

-13

(-1,0) (3,0)Page #12

Lesson 7.3

+ 2𝒙𝟐 - 4x

+ 4x - 8

Determine the product of the following expression.

2𝑥 − 4𝑥

+2


2𝑥2 − 4𝑥 + 4𝑥 − 8

2𝑥2 − 8

LikeTerms

(x + 2)(2x - 4)

Friday April 12, 2020 Work Period

Page #12Lesson 7.3

Friday April 12, 2020 Exit Ticket F(x) = (x + 2)(2x - 4) G(x) = 2𝑥2− 8 𝑎𝑛𝑑

Is (-2,0) a solution to the system?

Yes, because it is on both lines and both tables.

x F(x)

-2 0

-1 -6

0 -8

1 -6

2 0

Today’s Objective

Students will be able to multiply binomials.

Unit 7Lesson 3

Graph the polynomial f(x) = (x + 1)(x +4)

Write the Vertex (1, -4)

Is the Vertex a Minimum or Maximum?

Why? Vertex is at the bottom of the graph.

Minimum

Friday April 12, 2020 Activator

Page #15Lesson 7.4

Today’s New Vocab (1 of 4)Factor the polynomial f(x) = 𝑥2+ 5x + 4

x f(x)

-4 0

-3 -2

-2 -2

-1 0

BOX the Solutions

Can you get the factors from the graph? Yes How?Change the signs on the Solutions.

f(x) = (x + 1) ( x + 4) Page #15

Lesson 7.4

.

Solve for x when 𝑥2 + 5x + 4 = 0 ?

(x + 1) ( x + 4) = 0

(x + 1) = 0 ( x + 4) = 0

x = -1 x = -4 -1 -1 -4 -4

This graph will cross the x-axis at (-4,0) and (-1,0).

Set both parentheses equal to zero.

Solution

Factor x + 4 = 0 x + 1 = 0

Factor

Solution


Page #15Lesson 7.4

Today’s New Vocab (3 of 4)Graph the polynomial f(x) = −2(𝑥 − 1)2

x f(x)

-1 -8

0 -2

1 0

2 -2

3 -8

BOX the Zero’s

X = ___1(1,0)

Can the vertex also be a zero?

YESPage #15

Lesson 7.4

Today’s New Vocab (4 of 4)Graph the polynomial f(x) = 2𝑥3 − 12𝑥2 + 10𝑥

x f(x)

0 0

1 0

5 0

BOX the Zero’s

X = ___

X = ___

Write the solutions.

X = ___0

15 Page #16

Lesson 7.4

Wednesday April 24, 2020 Work PeriodCompare the graph of f(x) = 𝑥2 to the graph

of g(x) = (𝑥 − 2)2 + 3. Which two directions did the g(x) shift(move)? 2 right and 3 up

x f(x)

-2 4

0 0

2 4

x g(x)

0 7

2 0

4 7

f(x) g(x)

Wednesday April 24, 2020 Exit TicketWhat is f(6) – g(6)? 36 – 19 = 17

f(x) = 𝑥2 g(x) = (𝑥 − 2)2 + 3

f(6) = 36

g(6) = (6 − 2)2 + 3f(6) = (6)2

g(6) = (4)2 + 3

g(6) = 16 + 3

g(6) = 19

Show your work. Page #16

Lesson 7.4

Today’s Objective

Students will be able to graph quadratics.

Unit 7Lesson 4

Monday April 16, 2020 Activator

1

2

How do you graph radical equations?

Page #19Lesson 7.5

x

2 steps

(1 of 4)

Radical/Root

Definition


Facts

Page #19Lesson 7.5

• Opposite of an exponent• Fractional • exponent

𝑥

9 = 3 16 = 4

𝑥12 𝑥2

x𝑥3

A radical(root) is an operation to remove (undo) an exponent.

Today’s New Vocab (2 of 4)Perfect Squares

9 = 3

16 = 4

Calculate the (square) roots.

25 = 5

36 = 6

49 = 7

100 = 10

144 = 12


x f(x)

0 0

1 1

4 2

9 3

Graph the function f(x) = 𝑥How is this calculated?

f(x) = 𝑥

f(9) = 9

f(9) = 3 Page #19Lesson 7.5


x f(x)

-5 3

-4 4

-1 5

4 6

Graph the function f(x) = 𝑥 + 5 + 3

How did the graph shift?

5 units left3 units up Page #20

Lesson 7.5

Monday April 16, 2020 Work Period

.

Graph f(x) = 𝑥 + 2 over the domain −2 ≤ x ≤ 7.

x f(x)

-2 0

-1 1

2 2

7 3

Intervals have no ARROWS.

starts. ends.Is there shading on the graph?

No, it is an equation.

Page #20Lesson 7.5

Monday April 16, 2020 Exit Ticket

.

Evaluate f(-2) and f(7) when f(x) = 𝑥 + 2.

f(x) = 𝑥 + 2

f(-2) = (−2) + 2

f(-2) = 0

f(-2) = 0(-2,0) is a point

on the line.

f(x) = 𝑥 + 2

f(7) = (7) + 2

f(7) = 9

f(7) = 3(7,3) is a point

on the line.

Today’s Objective

Students will be able to graph quadratic (radical) equations.

Unit 7Lesson 5


Page #23Lesson 7.6

Can you take the (square root) of a negative number? NoWhy? Two of the same numberscannot multiply to be negative

Calculate −9

Error: non-real (irrational)

(3) (3) = +9(-3)(-3)= +9


Page #23Lesson 7.6

How do you solve radical equations?

You can (square) root both sides.

Solve. 𝑥2 = 36

x = 6

Check your

Work.

𝑥2 = 36

(6)2= 36

36 = 36

Yes, x = 6 is a solution.


Page #23Lesson 7.6

However, is x = 6 the only solution? No

𝑥2 = 36

(−6)2= 36

36 = 36

x = -6 is also a solution.

Check on the calculator.

Make a table for f(x) = 𝑥2 - 36

x f(x)

-6 0

6 0


Page #23Lesson 7.6

Solve the quadratic (number exp.) equation.

𝑥2 − 5 = 44

𝑥2 = 9

𝑥2 + 7 = 16

𝑥2 = 49

x = 3

x = −3

-7 -7

x = 7

x = −7

+5 +5x y

7 0

-7 0x y

3 0

-3 0


Page #24Lesson 7.6

Solve the quadratic (number exp.) equation.𝑥2

3= 27

4𝑥2 − 3 = 97

x y

9 0

-9 0x y

5 0

-5 0

4𝑥2 = 100

X = ±5

𝑥2 = 25

+3 +3

÷ 4 ÷ 4 𝑥2 = 81

X = ±9

(3) (3)


.

A landscaper is creating a square flower bed such that the length is L, feet. The area of the flower bed is 81 square feet. Write and solve an equation to determine length.

Let L = Length 𝐿2 = 81

𝐿 = 9The length of the

flower bed is 9 feet.

How many 1-foot stones are needed for the perimeter? 9+9+9+9 = 36 stones Page #24

Lesson 7.6


.

Determine the cost of the garden with tax.

Page #24Lesson 7.6

Stones (36) at $1.95 each

Flowers (25) at $3.95 eachMulch (6) at $3.33 each

Weed Barrier (2) rolls at $15.99 each

$220.91 (1.08) = $238.58Tax Final Cost

Today’s Objective

Students will be able to solving equations with

exponents using radicals.

Unit 7Lesson 6


Page #27Lesson 7.7

Solve for x. How do you remove the root? ( )2

4 = X

( )2 ( )23 = 𝑥 + 5

9 = x + 5-5 -5

Check your work.

3 = (4) + 5

3 = 93 = 3 Yes


Page #27Lesson 7.7

Graph g(x) = 3 − 𝑥 + 5. x g(x)-5 3

-4 2

-1 1

4 0

Is (4,0) a root?

Yes, it is on the table next

to a zero.


Page #27Lesson 7.7

Evaluate g(4) when g(x) = 3 − 𝑥 + 5.

g(4) = 3 − (4) + 5

g(4) = 3 − 9

g(4) = 3 − 3

g(4) = 0

x g(x)

-2 1.26

4 0

Is g(4) rational or irrational? Rational b/c

9 𝑖𝑠 𝑝𝑒𝑟𝑓𝑒𝑐𝑡.

Is g(-2) rational? NoIt has a decimals on the table.


Page #27Lesson 7.7

Graph f(x) = 1

3𝑥 + 4.

x f(x)

-4 0

5 1

Is (-4,0) a root?

Yes, it is on the table next

to a zero.


Page #28Lesson 7.7

Evaluate f(-4) when f(x) = 1

3𝑥 + 4.

f(-4) = 1

30

f(-4) = 0

x g(x)

-4 0

-2 0.47

Is f(-4) rational or irrational? Rational b/c

0 𝑖𝑠 𝑝𝑒𝑟𝑓𝑒𝑐𝑡.

Is f(-2) rational? No,It has a decimals on the table.

f(-4) = 1

3(−4) + 4


.

The number of people, p involved in recycling in a community is

modeled by the function p = 90 3𝑥 + 400, where x is the number of months the recycling plant has been open. How people were involved starting out? After 3 months? After 12 months?

x P(x)

0 400

3 670

12 940

Does this graph indicate growth or decay of this

recycling program? GrowthWhy? The people helping

are increasing.


.

Page #28Lesson 7.7

The number of people, p involved in recycling in a

community is modeled by the function p = 90 3𝑥 + 400. How many people will be helping after 4 years(48 months)?

p(x) = 90 3𝑥 + 400

p(48) = 90 3(48) + 400

p(48) = 90 144 + 400

p(48) = 90(12) + 400

p(48) = 880

x p(x)

48 880

The more helping hands the better.

Today’s Objective

Students will be able to graph complex radical equations.

Unit 7Lesson 7

Thursday May 2, 2020 Activator

#5: Evaluate the function when x = 8.

Page #29Unit 7 Review

Today’s New Vocab (1 of 4)#10: What is the product of (3x-3) and (x+1)?

Product means multiply


Today’s (2 of 4)#11: Make a table, graph.

12. Write the Solutions

x = -1 and x = 1



Today’s New Vocab (3 of 4)#17. Solve the quadratic equation for x.(𝑥 + 3)2 = 49

(x + 3) = 7x + 3 = 7

x = 4-3 -3

(𝑥 + 3)2 = 49

(x + 3) = -7x + 3 = -7

x = -10-3 -3

Today’s New Vocab (4 of 4)#14: Simplify the expression. Page #31

Unit 7 Review

#9: What is equivalent to 2𝑥2(4x + 5)?

𝐼𝑠 2𝑥2

𝑎 𝑓𝑎𝑐𝑡𝑜𝑟? YesPage #30

Unit 7 Review

Thursday May 2, 2020 Exit Ticket

Monday May 6, 2019 Activator • Please take out your Homework • Please take out your Classwork• Unit #7 Test: 10% Question #19• No work needed on #2• You must receive at least a 65%, or you

must stay after school to complete it.

• Tutoring: Mon 2:45-4:15, Wed 2:45-4:15

Today’s Objective

Students will be able to review objectives from Unit 7.

Unit 7Review

Tuesday March 17, 2020 Activator · What is the “Box Method?” It is a way to multiply with...

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