· Web viewTh 2/277-N4Compare Max/MinF.IF.4, A.SSE.3. COMMON CORE WARM UP. F 2/287-N5Nature of Graph, Even/OddF.BF.3, F.IF.4. COMMON CORE WARM UP & Collect HW Set #2. 1. M 3/2. PRACTICE

ALGEBRA 1

UNIT 7

(7 LESSONS + 1 PRACTICE + 1 QUIZ + 1 STUDY GUIDE + 1 TEST = 11 DAYS)

Date Lesson Plan Standard(s) Other

M 2/24 7-N1 Compare Linear vs. Quadratic, Graph F.IF.9, F.IF.7, Start Warm UpsParabolas, Graph Parabolas over Interval F.IF.4 & Hand Out HW Set #21

T 2/25 7-N2 Quadratic Word Problems F.BF.1

W 2/26 7-N3 Domain and Range, Max/Min, A.REI.10, A.REI.11, Warm Up Quiz

Axis of Symmetry, Find Zeros (Roots) F.IF.1, F.IF.5

Th 2/27 7-N4 Compare Max/Min F.IF.4, A.SSE.3 COMMON CORE WARM UP

F 2/28 7-N5 Nature of Graph, Even/Odd F.BF.3, F.IF.4 COMMON CORE WARM UP & Collect HW Set #21

M 3/2 PRACTICE Start Warm Ups

& Hand Out HW Set #22

T 3/3 QUIZ

W 3/4 7-N6 Quadratic-Linear Systems Word Problems F.BF.1 Warm Up Quiz

Th 3/5 7-N7 Transformations F.BF.3 COMMON CORE WARM UP

F 3/6 STUDY GUIDE COMMON CORE WARM UP & Collect HW Set #22

M 3/9 TEST

7 - N1Today, you will be able to:

Linear Equation:

Quadratic Equation:

This form is called the _______________________ of a quadratic equation.

The shape of the graph of a linear function is called a _____________.

The shape of the graph of a quadratic function is called a _____________.

1. Graph y=2x+1 .

**When graphing a non-linear function, you must include an

___________________________________.

2. Graph y=x2−6 x+8 .

3. Graph y =- x2 .

4. Graph y=3 x2+6 x−4 over the interval −3≤x≤1 .

5. Graph y=( x+2)2 over the interval −5≤x≤1 .

6. Graph y=x 2 +2 over the interval x≥0 .

7. Graph y=2x2−3 .

7 – N2Today, you will be able to:

1. Miranda has her boat docked on the west side of Casper Point. She is boating over to Casper Marina, which is located directly east of where her boat is docked. However, she has to boat around Casper Point to get to Casper Marina. Her boat’s distance, in feet, she travels north of

her starting point is modeled by , where t is the time traveled, in minutes. Graph the path of the boat over the interval 0≤t≤16 .

What is the maximum number of feet north that she traveled?

How long, in minutes, did it take her to reach Casper Marina?

2. Paul plans to have a rectangular garden adjacent to his garage. He will use 36 feet of fence to enclose three sides of the garden. The area of the garden, in square feet, can be modeled by

, where w is the width in feet.

On the set of axes below, sketch the graph of .

Explain the meaning of the point in the context of the problem.

3. A football player attempts to kick a football over a goal post. The path of the

football can be modeled by the function h( x )=− 1

225x2+ 2

3x

, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet. On the set of axes below, graph the function y=h( x ) over the interval 0≤x≤150 .

The goal post is 10 feet high and 40 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.


A parabola is said to open upward when it has a ____________________.

A parabola is said to open downward when it has a __________________.

The turning point of the parabola is called the ____________________.

The line drawn through the vertex is called the _______________________.

The x-intercepts are called ___________________ or _________________.

1. Graph f ( x )=x2+4 x+3 .

Does the above parabola open upward or open downward?

What is the minimum value of the above parabola?

What is the vertex of the above parabola?

What is the axis of symmetry of the above parabola?

What are the zeros of the above parabola?

2. Graph y=x2+6 x+5 .

What is the domain?

What is the range?

Is this a function?

Is this a one-to-one function?

Does the parabola open upward or downward?

What is the minimum value?

What is the vertex?

What is the axis of symmetry?

What are the zeros?

3. Graph f ( x ) =- x2−10 x−21 .

What is the domain?

What is the range?

Is this a function?



What is the maximum value?

What is the turning point?


What are the zeros?


1. Graph y=−x2+2 x+3


What is the vertex?


What are the zeros?

***YOU CAN DETERMINE THE PARTS OF THE PARABOLA WITHOUT THE GRAPH – JUST LOOK AT YOUR X/Y CHART!

2. Without graphing the parabola, use the x/y chart to determine the parts

of the parabola y=( x−4 )2−9.


What is the vertex?


What are the zeros?

3. Without graphing the parabola, use the x/y chart to determine the parts

of the parabola y=−x2+4 x+5.


What is the vertex?


What are the zeros?

4. Let f be the function represented by the graph below.

Let g be a function such that g ( x )=−1

2x2+4 x+3

.

Determine which function has the larger maximum value. Justify your answer.

5. The graph representing a function is shown below.

Which function has a minimum that is less than the one shown in the graph?

(1) y=x2−6 x+7 (3) y=x2−2 x−10

(2)y= (x+3 )2−6 (4) y= (x−8 )2+2

6. Alex launched a ball into the air. The height of the ball can be

represented by the equation h=−8 t 2+40 t +5 , where h is the height, in units, and t is the time, in seconds, after the ball was launched. Graph the equation from t = 0 to t = 5 seconds.

State the coordinates of the vertex and explain its meaning in the context of the problem.


1. Graph y+1=- 2

5x

What is the nature of the graph?

2. Graph y=x2−6 x+9

What is the nature of the graph when x<3?

What is the nature of the graph when x>3?3. Graph y=x2−8 x+7

What is the domain?

What is the range?

What is the vertex?


What are the zeros?

What is the nature of the graph when x>4 ?

4. A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball’s height always increasing?

(1) 0<x<2 .5

(2) 0<x<5 . 5

(3) 2 .5<x<5 .5

(4) x≥2

EVEN FUNCTION:

ODD FUNCTION:

Determine whether the following functions are even, odd, or neither:

UNIT 7 – PRACTICE #1

Answer the following multiple choice questions.

1. Which type of function is represented by the graph shown below?

(1) absolute value (3) linear

(2) exponential (4) quadratic

2. A swim team member performs a dive from a 14-foot high springboard. The parabola below shows the path of her dive.

Which equation represents the axis of symmetry?

(1) x=3 (2) y=3 (3) x=23 (4) y=23

3. The range of the function f ( x )=x2+2x−8 is all real numbers

(1) less than or equal to -9

(2) greater than or equal to -9

(3) less than or equal to -1

(4) greater than or equal to -1

4. Which function has the largest maximum?

Answer the following questions.

5. Graph the parabola y=x2+8 x+10 .

What quadrant does the vertex of this parabola lie in?

6. Graph y=x 2 +3 x+2 over the interval x≥0 .

7. On the set of axes below, draw the graph of y=x2−4 x−1 .

State the equation of the axis of symmetry.

Answer the following question.

8. Jamie launches a golf ball straight up into the air. The height of the

ball can be represented by the equation h=−5 t2+40 t , where h is the height, in units, and t is the time, in seconds, after the ball was launched. Graph the equation from t = 0 to t = 8 seconds.

State the coordinates of the vertex and explain its meaning in the context of this problem.

Complete the following.

9. Given the following parabola,



What is the vertex?


What are the roots?

Is this a function?


What is the domain?

What is the range?


QUADRATIC-LINEAR SYSTEM OF EQUATIONS consists of:

The graphs may intersect at ____________________________.

The graphs may look like:

1. Solve the system of equations. y=x2−6 x+6y=x−4

2. Let f ( x )=−2 x2 and g( x )=2 x−4 . On the set of axes below, draw the

graphs of y= f ( x ) and y=g (x ).

Using this graph, determine and state all values of x for which f ( x )=g( x ) .

3. A company is considering building a manufacturing plant. They determine the weekly production cost at site A to be A( x )=3 x2

while the production cost at site B is B( x )=8 x+3 , where x represents the number of products, in hundreds, and A(x) and B(x) are the production costs, in hundreds of dollars.Graph the production cost functions and label the site A and site B.

State the positive value(s) of x for which the production costs at the two sites are equal. Explain how you determined your answer.

If the company plans on manufacturing 200 products per week, which site should they use? Justify your answer.


The graphs of all functions in the FAMILY OF QUADRATIC

FUNCTIONS are __________________________.

Each family of functions has a __________________________________, the most basic function in the family.

The family of quadratic functions has the parent function ______________.

If you change the parent function by adding, subtracting, multiplying, or

dividing by a constant, you _____________________ the function and make a new function from the same family.

Changing the equation of a function also changes the graph of the function.

This change to the graph is called a _______________________________.

1. The graph below represents y=x2 .

Now graph y=x2−5 .

VERTICAL TRANSLATION:If k>0 , shift the parent function __________________.

If k<0 , shift the parent function ___________________.

2. The graph below represents y=x2 .

Now graph y= (x+4 )2 .

HORIZONTAL TRANSLATION:If h is added, shift the parent function __________________.

If h is subtracted, shift the parent function ___________________.3. The graph below represents y=x2 .

Now graph y =- x2 .

REFLECTION:Recall that the standard form of a quadratic equation is ________________.By changing the sign of a, you ________________ over the x-axis!

4. On your calculator, graph y=x2 and y=2 x2 . What happened to the graph?

On your calculator, graph y=x2 and y=1

2x2

. What happened to the graph?

STRETCHING AND SHRINKING:By changing the coefficient of a, your parabola can stretch or shrink!

If a>1 , then the parabola will vertically ___________________.If 0<a<1 , then the parabola will vertically _____________________.

6. The graph of the equation y=ax2 is shown below.

If a is multiplied by −1

2 , the graph of the new equation is

(1) wider and opens downward

(2) wider and opens upward

(3) narrower and opens downward

(4) narrower and opens upward

7. How does the graph of f ( x )=4 ( x+5 )2+3 compare to the graph of

g ( x )=x2?

(1) wider and its vertex is moved to the left 5 units and up 3 units(2) wider and its vertex is moved to the right 5 units and up 3 units(3) narrower and its vertex is moved to the left 5 units and up 3 units(4) narrower and its vertex is moved to the right 5 units and up 3 units

UNIT 7 STUDY GUIDE

7-N1 through 7-N5

1. Graph y=x2+2

What is the domain?

What is the range?

Is this a function?




What is the vertex?


What are the roots?

2. Graph y=−x2−8 x−7

What is the domain?

What is the range?

Is this a function?




What is the turning point?


What are the zeros?

What is the nature of the graph when x>−4 ?

3. The equation y=ax2+bx+c is graphed on the set of axes below.

Based on the graph, what are the roots of the equation ax 2+bx+c=0?

(1) 0 and 5

(2) 1 and 0

(3) 1 and 5

(4) 3 and -4

4. Identify the following as an even function, odd function, or neither.

5. Philip launched a ball into the air. The height of the ball can be

represented by the equation y=−1

4x2+8 x

, where y is the height, in feet, and x is the horizontal distance the ball travels, in feet. On the set of axes below, graph the function over the interval 0≤x≤32 .

Determine the vertex of the function. Interpret the meaning of this vertex in the context of the problem.

7-N6

6. On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.

y=x2+4 x−5y+1=x

7-N7

7. Which is the equation of a parabola that has the parent functiony=x2 , but whose vertex is shifted down 8 units?

(1) y=8 x2

(2) y =-8 x2

(3) y=x2+8

(4) y=x2−8

8. Which is the equation of a parabola that has the parent function y=x2 , but is wider and reflected about the x-axis?

(1)y=1

3x2

(2) y=3 x2

(3)y =- 1

3x2

(4) y =-3 x2

9. Compared to the graph of , the graph of

is the result of translating

(1) 2 units up and 3 units right

(2) 2 units down and 3 units up

(3) 2 units right and 3 units up

(4) 2 units left and 3 units right

Documents

· Web viewTh 2/277-N4Compare Max/MinF.IF.4, A.SSE.3. COMMON CORE WARM UP. F 2/287-N5Nature of Graph, Even/OddF.BF.3, F.IF.4. COMMON CORE WARM UP & Collect HW Set #2. 1. M 3/2. PRACTICE