HandOut 5.1, p. 263, Fig 5.6
Time
(seconds)
0
Distance
(feet)
2
1
First
Difference
p. 264, Fig 5.8
Second
Difference
x
y
0
0
5
1
2
2
8
2
4
3
11
3
6
4
14
4
8
5
17
p. 263, Fig 5.7
First
Difference
Second
Difference
p. 264, Fig. 5.8
Time
(seconds)
0
Distance
(feet)
2
1
First
Difference
Second
Difference
x
y
0
0
5
1
2
2
8
2
8
3
11
3
18
4
14
4
32
5
17
First
Difference
Second
Difference
p. 267, Fig 5.12
Time
(seconds)
0
Distance
(feet)
2
1
3.15
2
6.8
3
12.95
4
21.6
5
32.75
6
46.4
7
62.55
8
81.2
First
Difference
Second
Difference
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.2 p. 269, #12
x
y
0
First
Difference
Second
Difference
x
y
2
0
4
1
10
1
6
2
24
2
8
3
44
3
10
4
70
4
12
First
Difference
Second
Difference
p. 263, Fig 5.7
Time
(seconds)
0
Distance
(feet)
25
1
15
2
9
3
7
4
9
5
15
First
Difference
Second
Difference
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.3, p. 271, Fig 5.15
x
y
0
First
Difference
-p. 271, Fig 5.16
Second
Difference
x
y
6
0
4
1
5
1
6
2
10
2
8
3
21
3
10
4
38
4
12
First
Difference
Second
Difference
-p. 271, Fig 5.17
Speed
0
Reaction
Distance
0
Braking
Distance
0
Stopping
Distance
0
10
10
5
15
20
20
20
40
30
30
45
75
40
40
80
120
First
Difference
Second
Difference
50
60
70
p. 272, Fig 5.18
Speed
0
Stopping Distance
for Large Trucks
0
Stopping Distance
for Trains
0
10
10
15
20
20
40
30
30
75
40
40
120
First
Difference
Second
Difference
50
60
70
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.4, p. 273, Fig 5.19
x
-3
y = x2
x
p. 273, Fig 5.20
Preimage
y = x2
Image
y = x2 + 3
x
-2
-3
-3
-1
-2
-2
0
-1
-1
1
0
0
2
1
1
3
2
2
3
3
p. 274, Fig 5.22
x
Preimage
y = x2
x
Image
y = (x - 3)2
x
-3
0
-3
-2
1
-2
-1
2
-1
0
3
0
1
4
1
2
5
2
3
6
3
Preimage
y = (x + 2)
Image
y = x2 - 2
Preimage
y = x2
p. 275, Fig. 5.25
Image
2
Preimage
y = x2
p. 275, Fig. 5.23
p. 275, Fig. 5.24
x
p. 274, Fig 5.21
x
2
Preimage
2
y = -(x + 2)
y=x
Image
y = -x2
p. 276, Fig. 5.26
Image
y = 2x
x
2
Preimage
y=x
-5
-3
-3
-4
-2
-2
-3
-1
-1
-2
0
0
-1
1
1
0
2
2
1
3
3
2
Image
y = ½x2
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.5, p. 281, Fig 5.33
Time
5:00 a.m.
Time
Interval
0
Average
Speed (mph)
70
5:30 a.m.
1
50
6:00 a.m.
2
35
6:30 a.m.
3
25
7:00 a.m.
4
20
7:30 a.m.
5
20
8:00 a.m.
6
25
8:30 a.m.
7
35
9:00 a.m.
8
50
9:30 a.m.
9
70
First
Difference
Second
Difference
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.6, p. 291, #1
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
x2
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.7, p. 296, Fig. 5.39
Algebra
Tiles
a) Represent the function using tiles.
f(x) = x2 + 4x + 1
b) Group the x-terms using parentheses.
f(x) = (x2 + 4x) + 1
c) Find
1
2
of the coefficient of x.
Square this value, then add it to your
x-terms inside the parentheses.
f(x) = (x2 + 4x + ___) + 1
4
2
=2
22 = 4
d) You want to manipulate the equation, not
change its value. So, take the value from
step c) that you added and subtract it
outside the parentheses. Factor your
trinomial, and combine like terms to write
the vertex form.
To add 4, then, we also need to subtract 4.
f(x) = (x2 + 2x + 4) – 4 + 1
f(x) = (x + 2)2 – 4 + 1
Combine like terms.
f(x) = (x + 2)2 – 3
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.8, p. 297, Fig 5.40
Need chart from p. 297 here.
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.9, p. 301, Fig 5.43
Algebra
Sketch of Tiles
a) Group the x-terms using parentheses.
b) Factor out a 3 from both the x2
and x-terms.
c) Find ½ of the coefficient of x.
Square this value, then add it to the
x-terms inside the parentheses.
d) You want to manipulate the
equation, not change its value.
So, take the value from step c)
that you added, multiply it by the 3
that you factored out (distribute,
distribute!), and subtract it outside
the parentheses. Factor the
trinomial, and combine like terms
to write the equation in vertex
form.
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
5.10, p. 311, Fig 5.44
Graph
Factored Form
Vertex Form
Polynomial Form
y = x(x – 2)
y = (x – 1)2 – 1
y = x2 – 2x
y = (x – 2)(x + 1)
y = 2(x – 2)2 – 2
y = -½ x2 + 2
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.11, p. 312, Fig 5.45
General Form of
Equation
Critical Attributes
Preferred Method
of Solution
Factored Form
Vertex Form
Polynomial
Form
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.12, p. 313, Fig 5.46
Graph
Factored
Form
Algebra
Tiles
Vertex
Form
Polynomial
Form
1.
y = -3x2 + 6x
2.
p. 317, Fig 5.49
Number of
Points on
the Circle
2
p. 317, Fig 5.50
Number of
Lines Drawn
28
26
24
22
3
20
4
18
6
7
Number of Lines
5
16
14
12
10
8
6
4
2
1
2 3
4 5 6 7 8 9
Number of Points
10
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.13, p. 318, Fig 5.51
Coordinates of
Points in
Original
Drawing
(-8, 0)
p. 321, Fig 5.52
Corresponding
Coordinates of
Points in
Reflected Drawing
Original
Reflected
Coordinates Coordinates
(2, 2)
(-9, -2)
(2, 4)
(-3, -2)
(-1, 4)
(-4, 0)
(-3, 1)
(-4, 8)
(-6, -1)
(-6, 10)
(-5, -4)
(-8, 8)
(-3, -6)
(1, -5)
(2, -2)
(4.5, 0.5)
p. 325, Fig 5.56
Function
p. 325, Fig 5.57
Domain
Range
Function
x≥0
y≥0
y= x
y= x +2
x≥0
y≥2
y= x −3
x≥0
y ≥ -3
y= x
Describe
Changes to
the Parent
Function
Parent
Describe
Changes to
the Parent
Function
Parent
Domain
Range
x≥0
y≥0
y = x+3
x ≥ -3
y≥0
y = x−2
x≥2
y≥0
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.14, p. 325, Fig 5.58
Function
Describe
Changes to
the Parent
Function
Parent
p. 325, Fig 5.59
Domain
Range
Function
x≥0
y≥0
y= x
y = 0.5 x
x≥0
y≥0
y=2 x
x≥0
y≥0
y= x
Describe
Changes to
the Parent
Function
Parent
Domain
Range
x≥0
y≥0
y=− x
x≥0
y≤0
y = −0.5 x
x≥0
y≤0
p. 327, Fig 5.60
10
9
8
7
6
5
4
3
2
1
1
2
3
4 5
6
7
8
9 10
p. 329, Fig 5.62
Length of
Pendulum (cm)
15
Time for 10
Swings (sec)
Period
(sec)
25
35
45
55
65
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.15, p. 331, Fig 5.63
p. 331, Fig 5.64
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Handout 5.16, p. 335, Fig 5.69
Time (t)
Distance (d)
0s
0.4 s
0.6 s
0.8 s
1.0 s
1.2 s
Practice Problems p. 339, Fig 5.72
x-value
y-value
First
Difference
Second
Difference
0
1
2
3
4
5
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company
Transparecy 5.17, p. 276, Fig 5.27
Modeling With Mathematics: A Bridge to Algebra II Chapter 5 Handouts/Transparencies
© 2006 W.H. Freeman and Company