· Web viewW 3/77-N6Quadratic-Linear Systems Word ProblemsF.BF.1 Th 3/87-N7TransformationsF.BF.3 Warm Up Quiz F 3/9STUDY GUIDE Collect HW Set #21 M 3/12TEST 7 - N1 Today, you will

ALGEBRA 1

UNIT 7

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

Date Lesson Plan Standard(s) Other

M 2/26 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 #20

T 2/27 7-N2 Quadratic Word Problems F.BF.1

W 2/28 7-N3 Domain and Range, Max/Min, A.REI.10, A.REI.11, Axis of Symmetry, Find Zeros (Roots) F.IF.1, F.IF.5

Th 3/1 7-N4 Compare Max/Min F.IF.4, A.SSE.3

F 3/2 7-N5 Nature of Graph, Even/Odd F.BF.3, F.IF.4 Collect HW Set #20

M 3/5 PRACTICE Hand Out HW Set #21

T 3/6 QUIZ

W 3/7 7-N6 Quadratic-Linear Systems Word Problems F.BF.1

Th 3/8 7-N7 Transformations F.BF.3 Warm Up Quiz

F 3/9 STUDY GUIDE Collect HW Set #21

M 3/12 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. A ball is thrown into the air from ground level. It travels a path represented by y =- x2+8 x , where y represents the height of the ball, in feet and x represents the time, in seconds. Graph the path of the ball from x = 0 to x = 8 seconds.

What is the maximum height achieved by the ball?

2. The height of a cannonball, in feet, is described by the equation h=−4 t2+64 t , where t is the time in seconds since it was fired into the air. Graph the path of the cannonball over the interval 0≤t≤16 .

At what time is the cannonball at its maximum height?

At what time will the cannonball fall to the ground?

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:


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 time, in seconds after the ball was launched. 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. Which of the following equations will transform f ( x ) into g ( x ) , where g ( x ) is narrower and shifted left 6 units?

(1)g ( x )=1

3f ( x−6 )

(2)g ( x )=1

3f ( x+6 )

(3) g ( x )=3 f ( x−6 )

(4) g ( x )=3 f ( x+6 )

Documents

· Web viewW 3/77-N6Quadratic-Linear Systems Word ProblemsF.BF.1 Th 3/87-N7TransformationsF.BF.3 Warm Up Quiz F 3/9STUDY GUIDE Collect HW Set #21 M 3/12TEST 7 - N1 Today, you will