Algebra 2 2014-2015

Second Six Weeks October 6 – November 14, 2014

Monday Tuesday Wednesday Thursday Friday

October 6 B Day 7 A Day 8 B Day 9 A Day 10 B Day 3.2 Substitution and Elimination -from contexts, write equations, determine best method to use, define variables and solve. -2 variable

3.3 Substitution and Elimination -continue solving -3 variable (NEW)

3.4 Solving systems with matrices -Setting up matrices from systems of equations - solving systems with matrices

13 14 A Day 15 B Day 16 A Day 17 B Day

No School

Professional

Development

Day

Flex Day 3.5 Linear Programming -Writing Equations and inequalities -Graphing Restraints -Find critical points and calculate max and mins

20 A Day 21 B Day 22 A Day 23 B Day 24 A Day

Unit 3 Elaboration/Flex Day

4.1 Representations of Quadratic Functions -analyze & predict using quadratic data -make scatterplot -graph and look at tables -quadratic regression

27 B Day 28 A Day 29 B Day 30 A Day 31 B Day 4.1 Representations of Quadratic Functions -analyze & predict using quadratic data -make scatterplot -graph and look at tables -quadratic regression

4.2 Transforming Quadratics -up/down, left/right, horz/vert stretch/compression -domain/range in inequality, interval & set notaion Begin 4.3

4.3 Three forms of a Quadratic -discuss factored, vertex, and standard form, their characteristics and uses -complete the square to move from standard to vertex

Nov 3 A Day 4 B Day 5 A Day 6 B Day 7 A Day 4.4 Parabola Conic Sections -graph and identify key attributes (vertex, focus, directrix, axis of symmetry, direction of opening) -write equation given attributes

Unit 4 Elaboration/Flex

10 B Day 11 A Day 12 B Day 13 A Day 14 B Day

Reteach/Retest 4A

4.6 Solve by graphing -use calculator -solve linear & quadratic intersection(s) (NEW) -Look at zeros/roots/x-intercepts and solutions on a graph by hand and on calculator

UNIT 3 TEST

UNIT 4A

TEST

PSAT

1

Algebra 2 4.2 Transformations of Quadratic Name:_____________________

Transformation Stations Worksheet

Remember: Use the Vertex Form for a Quadratic Function 2

( )y a x h k= − + to

translate Quadratic Functions from the Parent Function 2

y x=

Station 1:_________________________

Station 2:__________________________

Station 3:__________________________

Station 4:__________________________

Station 5:__________________________

Station 6:__________________________

2

Algebra 2 4.2 Transformations of Quadratic Name:_____________________

CONCLUSION: What happens when you change the value of……..

a:

h:

k:

2( )y a x h k= − +

3

Algebra 2 4.2 Transformations of Quadratic

Name:_____________________

Page 1 of 4

For #1-4, Graph each of the following equations. State the domain, range and

axis of symmetry for each.

1) 122 xy 2) 12 2 xy

Transformations:__________________ Transformations:___________________

D:__________R:_________AOS:_____ D:__________R:__________AOS:_____

3 points (___,___),(___,___),(___,___) 3 points (___,___),(___,___),(___,___)

3) 132 xy 4) 23

2

1 xy

Transformations:__________________ Transformations:___________________

D:__________R:_________AOS:_____ D:__________R:__________AOS:_____

3 points (___,___),(___,___),(___,___) 3 points (___,___),(___,___),(___,___)

4

Algebra 2 4.2 Transformations of Quadratic

Name:_____________________

Page 2 of 4

____ 5. Which graph shows a function y = x2 + c when c < -1?

____ 6. The graph of y = 11x2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c?

a. c > 0 b. c < 0

c. c = 0 d. c = 11

____ 7. Shirley graphed a function of the form y = ax2 + c. She then

translated the graph 8 units up, resulting in the function 53

2 2 xy .

Which of the following best represents Shirley's original function?

a. 133

2 2 xy

b. 133

2 2 xy

c. 33

2 2 xy

d. 33

2 2 xy

____ 8. If , how does the graph of compare to the graph of

?

a. The graph of is below the graph of .

b. The graph of is above the graph of .

c. The graph of is narrower the graph of .

d. The graph of is wider the graph of .

5

Algebra 2 4.2 Transformations of Quadratic

Name:_____________________

Page 3 of 4

____ 9. The graph of a function of the form is shown below.

If the graph is translated only up or down to include the ordered pair (6, 7),

which of the following equations best represents the resulting graph?

a.

c.

b.

d.

____ 10. The grid below shows parabolas A and B of the form .

How are the parabolas A and B related?

a. Parabola A is narrower than parabola B. b. Parabola A is wider than parabola B.

c. All the points on parabola A are 7 units below the corresponding points on parabola B.

d. All the points on parabola A are 7 units above the

corresponding points on parabola B.

6

Algebra 2 4.2 Transformations of Quadratic

Name:_____________________

Page 4 of 4

11. Given the functions f(x) and g(x) as described in the following tables: f(x) g(x)

Describe the transformation from f(x) to g(x) in f(x) form.

12. Given the functions f(x) and g(x) as described in the following tables:

f(x) g(x)

Describe the transformation from f(x) to g(x) in f(x) form.

13. Describe two different transformations that would make the parabola

pass through the point (-2, -3).

14. Given 2( ) 2 6f x x write the equation of g(x) using the transformation

g(x) = f(x + 3) – 4.

X Y

1 8

2 5

3 4

4 5

X Y

-1 5

0 2

1 1

2 2

X Y

-4 -4

-3 -5

-2 -4

-1 -1

X Y

-2 5

-1 2

0 1

1 2

7

Algebra 2 4.3 Three Forms of a Quadratic

Name:_____________________

1. A hawk is diving down to catch a rabbit and carry it back to his nest. The path

is modeled by a quadratic. Three people have attempted to model the path and given you the following equations:

Enter the functions into your calculator and graph:

S(x) = 822 xx

F(x) = 24 xx

V(x) = 912x

a) What do you notice about the three graphs?

b) Verify algebraically that S(x) and F(x) are equal by solving the following equation:

S(x) = F(x) x2 – 2x – 8 = (x – 4)(x + 2)

c) Verify algebraically that S(x) and V(x) are equal.

d) Find the following critical attributes:

Vertex:___________

Roots:____________

y-intercept:________

8

Each of the 3 forms of quadratic equations can be identified by the critical

attributes above. Which equation tells you which attribute? Match them below.

Standard Form S(x) Vertex

Factored Form F(x) Roots

Vertex Form V(x) y-intercept

2. Now an archer shoots his bow at a barbarian on Clash of the Clans, making a parabolic path.

Graph the following three equations:

F(x) = 2(x + 6)(x – 2)

V(x) = 2(x + 2)2 – 32

S(x) = 2x2 + 8x –24

a) What value do you notice is the same in all three equations?

b) List the critical attributes of the quadratic function and match each attribute

with one of the equations.

c) Verify algebraically that S(x) and F(x) are equal.

d) Verify algebraically that S(x) and V(x) are equal.

9

Algebra 2 4.3 Three Forms of a Quadratic

Name:_____________________

The following is a picture of a Quadratic. Label the:

Roots: (r1, 0) and (r2, 0)

Vertex (max/min): (h, k)

y-intercept: (0, c)

Write the three forms of this Quadratic. Use “a” for your a value. These equations will

be the general forms for Standard, Vertex, and Factored forms of a Quadratic.

Standard form: __________________________________________________

Vertex form: ____________________________________________________

Factored form: __________________________________________________

10

Algebra 2 Elaborate 4.3 Three Forms of a Quadratic

Name:_____________________

Graph the given data and then write the equation for the quadratic in the three

forms we have learned. (F is factored form, V is vertex form, and S is standard form)

1) Vertex: (3, -4)

Roots: (1, 0) and (5, 0) Y- intercept: (0, 5)

a = 1

F(x) =

V(x) =

S(x) =

2) A baseball is thrown from 5 feet above the ground. The ball reaches a maximum height of 9 feet after 2 seconds. The ball lands on the ground 5 seconds

after it was thrown.

F(x) =

V(x) =

S(x) =

3) Given the following two graphs, write the three equations that represent the graphs.

a)

F(x) =

V(x) =

S(x) =

11

b)

F(x) =

V(x) =

S(x) =

5) Given the following tables, what are the roots of the equation?

x y

10 2

11 0

15 3

16 0

6) Given the following tables, what are the roots of the equation?

If there aren’t any zeros in the y column, we can probably get a really good guess

as to where the zeros are.

x y

-6 22

-5 5

-4 -8

1 -13

2 -2

3 13

12

Algebra 2 4.3 Three Forms of a Quadratic

Name:_____________________

1. The following equations are three forms of the same quadratic equation.

S(x)= x2 – 2x – 15 F(x) = (x + 3)(x – 5) V(x) = (x – 1)2 – 16

Find the following and identify the form of the equation that gives that information:

a) y-intercept

b) vertex

c) roots

2. Rewrite the following equations in standard form:

a) y = 3(x – 1)(x + 2) b) y = -1(x + 3)2 – 4 c) y = 2(x – 4)2 + 5

3. Tommy shot a bottle rocket off the top of his garage, which is 26 feet from the

ground. The bottle rocket reaches a maximum height of 98 feet after six seconds and hits the ground after 13 seconds.

a) Sketch a graph of the height as a function of time. Label the axes, vertex, y-

intercept, and the positive x-intercept.

b) Write the equation for this problem situation in the three forms. Be sure to find

the “a” value within the equation.

Factored Form: F(x) =

Vertex Form: V(x) =

Standard Form: S(x) =

13

-2 2 4 6 8 10

-15

-10

-5

5

10

15

5 10 15 20 25 30 35-10

10

20

30

40

50

60

70

80

90

4. Tiger Woods tees off from the top of a hill. A diagram of the situation is shown

below on a coordinate grid.

a) Given a = -.005, write the equation in factored form.

F(x) =

b) Find the maximum height of the ball and label the vertex on the graph.

c) Write the equation in the vertex and standard form.

V(x) =

S(x) =

d) If the origin is considered the base of the hill, how high is the hill?

5. Given the following two graphs, write the three equations that represent the graphs.

Factored Form: F(x) = Factored Form: F(x) =

Vertex Form: V(x) = Vertex Form: V(x) =

Standard Form: S(x) = Standard Form: S(x) =

(14, 121)

(2,-12)

(340, 0) x = 160

( __ , __ )

(3, 0) (25, 0)

(0, 0) (4, 0)

14

Algebra 2 8.3 Explain: Parabolas PPT

Page 1 of 4

Parabola – set of all points equidistant from a fixed line (_____________)

and a fixed point (______________). ___________ – midpoint of

segment from focus to directrix.

_____________________________ – line through focus and vertex

Vertical Parabola Horizontal Parabola

Form: _______________ Form: ____________

p: distance from vertex to _________ and from vertex to __________.

Write equation in standard form by completing the square.

Ex1: 22 4 8 8 0y x x

Decide whether parabola has vertical or horizontal Axis of Sym. and

which way the graph opens. Ex2: -6x2 = 3y Ex3: (y – 4)2 = 3x + 1 Ex4: 2y = (x + 1)2

Given the following information, write the equation of the parabola. 5. Vertex (-2, 5); p = -1/2; Vertical Axis of Symmetry

6. Vertex (1, -3); p = 1/8; Vertical Axis of Symmetry

7. Vertex (6, -1); p = -1/12; Horizontal Axis of Symmetry

8. Vertex (-5, -7); p = 1; Horizontal Axis of Symmetry

p

2p

2p

p

15

Algebra 2 8.3 Explain: Parabolas PPT

Page 2 of 4

9. 10.

Vertex: Vertex:

Focus: Focus:

Directrix: Directrix:

Axis: Axis:

Equation: Equation:

11. 12.

Vertex: Vertex:

Focus: Focus:

Directrix: Directrix:

Axis: Axis:

Equation: Equation:

16

Algebra 2 8.3 Explain: Parabolas PPT

Page 3 of 4

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

Find the vertex, focus, and directrix and sketch the graph.

13. 2

12 1 3y x 14. 2

4 3 5x y

Vertex: Focus: Vertex: Focus:

Directrix: Directrix:

Find the equation, given the following information.

15. Vertex (-3, 6) Focus (5, 6)

16. Vertex (2, –1) Directrix: x = 5

17. Directrix: y = 5 Focus (–3, 1)

18. Where are parabolas used?

17

Algebra 2 8.3 Explain: Parabolas PPT

Page 4 of 4

2( ) 4 ( )x h p y k 2( ) 4 ( )y k p x h

Vertex (h, k) (h, k)

Axis of symmetry x = h y = k

Focus ,h k p ,h p k

Directrix pky phx

Direction of opening up/down left/right

Length of Latus Rectum

(LR)

1

a or 4p

1

a or 4p

P

p

a4

1

pa

4

1

Vertex: ( ___, ___ )

Focus ( ___, ___ )

Axis of Symmetry: x = ___

LR: ______

Directrix: y = _____

p

18

Algebra 2 8.3 Evaluate: Parabolas

Name _______________________

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

f(x)

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

f(x)

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

f(x)

Write the equation of the parabola in standard form:

1. 2 2 4 3 0x x y 2. 2 12 4 8 0y x y

Decide whether the parabola has a vertical or horizontal axis:

3. 8x2 = y 4. 3x = 4y2

Find p, the focus, and the directrix of the parabola:

5. 21

4y x 6.

28( 1) 6x y

Match the equation with the graph:

7. y2 = -2x ______ 8. x2 = 2y ______ 9. x2 = -2y ______

A) B) C)

19

Algebra 2 8.3 Evaluate: Parabolas

Name _______________________

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

f(x)

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3-2-1

123456789

x

f(x)

Graph the following equations:

10. 2( 2) = 16( 1)y x 11. 2( 1) = -12( 3)x y

Write the equation of the parabola in standard form.

12. Vertex: (3, -2) Focus: (5, -2)

13. Vertex: (2, 2) Directrix: y = 5

14. Steve Jobs has asked you to do some consulting on a secret project for Apple. The next ipod, the ipod wireless needs to have a parabola inside of it

to communicate with the Apple satellite system. Mr. Jobs needs you to write the equation of a parabola with vertex at (5,1) and directrix x = 6.

20

Transforming Quadratics

Using a, h, and k to transform Quadratics

The quadratic parent function is .

Its Vertex is .

The quadratic function in the vertex form is ____ ______________(a, h, k). Describe

the effect of each variable.

(-): _________________________ h: ____________________________

0 < a < 1: _____________________ k: ____________________________

a > 1: ________________________

A. A quadratic reflected over the x axis B. Given the following function, give an

Translated 4 units up and 6 units to example of a number that would make

the left from the parent function. the graph wider. 21

( ) 3 42

f x x

C. Use transformations to write the equation

of the following graph.

D. Given the functions f(x) and g(x) as described in

the following tables:

f(x)

X Y

1 8

2 5

3 4

4 5

g(x)

X Y

-1 5

0 2

1 1

2 2

Describe the transformation from f(x)

to g(x) in f(x) form.

21

Representations of Quadratics

Use patterns to write equations

How can we tell?

A. List out the steps to writing an B. The following table shows the growth

equation using the calculator of bacteria in a lab. Write the quadratic equation that best models this scenario.

2 3 4 5

92 216 388 602

C. Use stat regression to write the equation to D. Given the pattern, write the equation the following graph. 17, 28, 43, 62, 85

+1 +1 +2 +1 +1 +1 +1 +1

x 3 4 5 6 7

y -1 1 7 17 31

x 1 2 3 5 6

y 4 8 12 20 24

+4 +4 +8 +4 +2 +6 +10 +14

+4 +4 +4

It is Definitely Linear!

It is Definitely Quadratic!

22

B. Mrs. Ballero’s pet lemur made the following jump. Give the reasonable range for the

function. Modeled by 214

3y x x

Graphing Quadratics

A. Nicole shot her rocket into the air from

the floor. It landed next to Kelly’s desk 12 seconds later. Write the equation. a=-16

C. Write the equation to the axis of symmetry

for the equation 2( ) 2 15f x x x

D. Reflect the following graph across the x axis.

23

B. The following equation is in the vertex form. Write it in standard form.

Critical Attributes

Use the your knowledge of quadratics to find the critical attributes

2( ) ( )V x a x h k

A. Write the equation to the following scenario

Hit over a 10 foot fence after 50 secs. He hit from a height of 6 feet.

C. What is the x value to the max of the graph

that has the roots (-2,0) and (6, 0)?

X Y

-3 0

-1 -4

0 -4.5

1 -4

3 0

2( )s x ax bx c 1 2( ) ( )( )f x a x r x r

What do I know from

this?

What do I know from

this?

What do I know from

this?

2

( ) 4 3V x x

D. Write the 3 forms of the quadratic from the table.

24

B. Factor

Factoring Quadratic

A. Factor 2 7 12x x

C. Factor to put in standard form and give the

roots. 2 20y x x

2( ) 100f x x

D. Factor to put in standard form and give

the roots. 2 5 6y x x

Find the

multiples of ac.

2y ax bx c

Find the 2 that

sum to be b.

Put in the parenthesis as

such (x+____)(x+ ).

You Factored!

25

B. What are the roots to the following function

3 Names of the Quadratic

Use the 3 forms to represent quadratics

2( ) ( )V x a x h k

A. Circle the part of each form that tells if the

parabola is concave up or down.

2( ) ( )V x a x h k

C.Use the table below to find the information.

X Y

-3 0

-1 -4

0 -4.5

1 -4

3 0

2( )s x ax bx c 1 2( ) ( )( )f x a x r x r

What do I know from

this?

What do I know from

this?

What do I know from

this?

19

( ) 4 17100

f x x x

D. Write the 3 forms of the quadratic for the graph below.

Vertex:

Roots:

2( )s x ax bx c

1 2( ) ( )( )f x a x r x r

26