Bellwork

Bellwork Solve for x

• 5x-4=3x+10• x2-3x-10=0• 4x-3+5x-7+8x-12=360

Clickers

Bellwork Solution Solve for x

5x-4=3x+10

.1.75

.7

.14

ABC


x2-3x-10=0

. 2,5

.2, 5

.1, 10

. 1,10

ABCD


4x-3+5x-7+8x-12=360

.11.36

.15.59

.19.88

.22.47

ABCD

CHAPTERS 8 & 10 MASTERY TEST ON WEDNESDAY

Question #1Solve for x

.145

.210

.720

ABC

105

75

145130120

x


.17.3

.18.7

.54.7

ABC

3x

5x

35

5385

2x

Question #3What is the value of x?

3 3x

33

.10

.12

.13

ABC

Question #4What is the value of x?

x 105

.30

.45

.75

.105

ABCD

Question #5What value of x makes the object a rectangle?

15x 2 8x

.7

.7.67

.23

ABC

Question #6Solve for x?

5 2x 2 13x .2.14.3.67.5

ABC

Question #7For what value of x, does the trapezoid become isosceles

.23

.24.3

.25

ABC

71o 3x-2

Question #8What is the measure of the missing angles?

.30

.90

.100

ABC

120o

B15

A

40o

Question #9Solve for the midsegment AB

.3

.28

.56

ABC

A B

31

25


.6.8

.13

.14.8

ABC

A B

3x-4

2x+1

31

Question #11What is the name of this object

A.TrapezoidB.IsoscelesTrapezoidC.KiteD.Rectangle

Question #12What is the name of this object?

A.RhombusB.RectangleC.Square

Question #13Which quadrilaterals have perpendicular bisectors?

A. Kites, Trapezoids, RhombusesB. Rhombuses, Rectangles, SquaresC. Kites, RhombusesD. Kites, Rhombuses, Squares

Question #14Which quadrilaterals have congruent bisected diagonals?

A. Kites, Rectangles, SquaresB. Rhombuses, Rectangles, SquaresC. Rectangles, RhombusesD. Rectangles, Squares

Homework Chapter 8 Test (pg 564)

1-11, 14-17

Bellwork Solve for x

5x-5=2x+10 2x2-6x-8=0 4x+5+7x+8x-12=360

Clickers


5x-5=2x+10

..6

.2.14

.5

ABC


2x2-6x-8=0

. 1,4

.1, 4

.2, 8

. 2,8

ABCD


4x+5+7x+8x-12=360

.14.89

.18.58

.19.32

.21.55

ABCD

CHAPTERS 8 & 10 MASTERY TEST ON FRIDAY

Question #15Which is a chord of the circle below?

A

B

C

D

E

FGH

.

.

.

.

.

A DH

B DG

C GF

D CG

E BF

Question #16Which is the point of tangency of the circle below?

A

BC

D

EF

G

H

.

.

.

.

.

A ABBC GD DE I

I

Question #17 What is the measure of Arc AB

150o

A

C

B

80o

D

.75

.80

.150

.230

ABCD

Question #18 What is the measure of Arc ADB

150o

A

C

B

80o

D

.80

.130

.150

.210

ABCD

Question #19 Solve for x

5x-12

3x+2

.1.75

.2.25

.5

.7

ABCD


B

A

.90

.135

.270

.360

ABCDxo

Question #21 What is the measure of angle ABC

78o

A

C B

D

.39

.78

.156

ABC


J K

M L

.17.8

.18.2

.44.5

.45.5

ABCD6x+4o

4x-2o

Question #23 What is the measure of angle ACD, if arc CD measures

160o

65o

A

C

B

D

.35

.65

.130

ABC


125o

A

C

B

D

.20

.145

.290

ABC

E

165o


65o

A

B

D

.65

.130

.260

ABC

195o

xo


x

A

CB

D

56.

.1

.6

ABC

x+5

3

2


x

6

x

6 84.2

.3 45

. 6

A

B

C

Homework Worksheet

#20

A

B

VUP Q

60AVB

ExampleWhat theorem would we use to show that the

quadrilateral is a parallelogram?

2525 ..8.7.8.8.8.9.8.10

A DefBCDE



20

20

16

16

.

.8.7

.8.8

.8.9

.8.10

A DefBCDE



120

120

.

.8.7

.8.8

.8.9

.8.10

A DefBCDE

60

60



.

.8.7

.8.8

.8.9

.8.10

A DefBCDE

ExampleWhat value of x, makes the quadrilateral a

parallelogram?

5 10x 45 .9

.11

.40

ABC

Proving via CoordinatesWe can also prove that an object is a quadrilateral if we’re

given the coordinates of the vertices by

1. Proving that both sets of sides are congruent 2. Proving that two sides are congruent and parallel3. Proving that both sets of sides are parallel

Proving congruency is easy via the distance formula, so let’s look at this one

An example…Find all of the angles given the listed angle measure

130

2

1

4

7

6

5

8

Another example…We see these angles used in figures as well

Find x & y

20180918063

yyyy

3y

2x

6y

45902180902

xx

x

Or in a proofWrite a proof

CDABGiven ||:3

2

1

4

7

6

5

8

A B

C Darysupplement 8,3

:Prove

Another example…Find x & y

2y 5x

14x-10

Where does this come from? How did we get this formula?

212

212

2212

212

222

)()(

)()(

yyxxc

cyyxx

cba

(x1,y1)

(x2,y2)

x2-x1

y2-y1

a=

b=c

Why is there not a plus or minus in front of

this?

Practical Example

Graphing We can also plot several iterations to see the effect of

a scalar (or leading coefficient) attached to the term This scalar makes the equation y=ax2

Y

X

x y=x2

1 12 4

3 9

-1 1

-2 4

-3 9

y=2x2

28

18

2

8

18

y=1/2x2

.52

4.5

.5

2

4.5

Graphing These graphs lead us to understand

a fundamental of graphing If a>1, the graph stretches If a<1, the graph flattens

Y

X

Graphing Let’s look at what happens when a<0

Y

X

x y=x2

1 12 4

3 9

-1 1

-2 4

-3 9

y=-x2

-1-4

-9

-1

-4

-9

Therefore we see that if a<0, the graph is mirrored over

the x-axis

Fundamental Rules At this point we see some fundamental rules

of quadraticsIf the leading coefficient is positive (a>0)

○ Concave up (cupped upwards)If the leading coefficient is negative (a<0)

○ Concave down (cupped downwards)

Graphing Let’s look at one last thing

What do you think happens when we add a constant?

Y

X

x y=x2

1 12 4

3 9

-1 1

-2 4

-3 9

y=x2+2

36

11

3

6

11

y=x2-3

-21

6

-2

1

6

Therefore we see that the constant dictates the height of the function on the y-axis

Fundamental Rules At this point we see some fundamental rules

of quadraticsIf the leading coefficient is positive (a>0)

○ Concave up (cupped upwards)If the leading coefficient is negative (a<0)

○ Concave down (cupped downwards)A constant added indicates the y-coordinate of the

vertex

Example Graph

2

41 xy

Y

X

Practical example An average Major League outfielder throws the ball about

approximately 75 miles per hour when they are trying to get the ball into the infield quickly. Assuming ideal conditions, if the ball is thrown straight up into the air, after how many seconds will it return to the player?

)11016(00110160

2)(

2

002

tttt

htvtgth

0tsec8.6

110160)11016(

tt

t

Our final answer 6.8 seconds after it was thrown

Implausibleanswer

75 mph in ft/s

Zero-Product Property This works no matter what the binomial

0)93)(42( xx

242

0)42(

xx

x

3930)93(

xx

x

Our final answer is x=-2 & 3

Bellwork

Documents

Transcript of Bellwork