Unit 9 The Birthday Party Pinata

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Unit 9 The Birthday Party Pinata Warm-up

Evaluate each of the following expressions for x
5 1) 3x 2) 7x 5 3) 9 x2 4) (2)x2
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Unit 9 The Birthday Party Pinata

BP-15 Graphing Square Roots On your resource
page. a) Graph y vx. Record your points in the
table on the resource page. b) Try x -3 in the
rule. What is the result? Explain.
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Unit 9 The Birthday Party Pinata

BP-15 Graphing Square Roots On your resource
page. c) Describe the possible values for x that
will yield solutions for the rule y vx. d) What
y values are possible? e) Describe your graph in
words.
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Unit 9 The Birthday Party Pinata

BP-21 You can solve for x in the equation x2
8x 12 0 but not for the expression x2
8x 12
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Unit 9 The Birthday Party Pinata

BP-21 a) Explain why using a complete sentence.
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Unit 9 The Birthday Party Pinata
For each of the following, decide if there is
enough information to solve for the variable. If
there is, then do so. If not, merely factor and
move on to the next part. b) b2 4b 4 c) b2
5b 4 d) b2 10b 21 0 e) b2 6b 5
0 f) b2 17b 16

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Unit 9 The Birthday Party Pinata

BP-22 Equations (d) and (e) in problem BP-21
each had two solutions. What do these solutions
represent on the graph of the equation? What
shape is each graph?
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Unit 9 The Birthday Party Pinata
BP-24 With your study team, find the minimum
amount of rope the prince needs. (Assume they
need an extra 1.5 feet of rope at each end in
order to tie the rope.) Write a complete
explanation for the prince, including a diagram
that shows how to determine the minimum length of
the rope needed.

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Unit 9 The Birthday Party Pinata
BP-25 On a baseball diamond, the bases are 90
feet apart. (Every baseball diamond is a square.)
How far is it from home plate directly to second
base? Sketch and label a diagram. Use it to write
an equation, then solve the equation.

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Unit 9 The Birthday Party Pinata
BP-26 A 10 foot ladder is leaning against a tree.
The foot of the ladder is 3.5 feet away from the
base of the tree trunk. a) Draw a diagram and
label the ladder length and its distance from the
tree.

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Unit 9 The Birthday Party Pinata
BP-26 A 10 foot ladder is leaning against a tree.
The foot of the ladder is 3.5 feet away from the
base of the tree trunk. b) How high on the tree
does the ladder touch? Write an equation to solve
it.

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Unit 9 The Birthday Party Pinata

5 / 310 / BP 30-32
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Unit 9 The Birthday Party Pinata Warm-up

Multiply each expression out. 1) (x 1)(2x
5) 2) x2(x 2) 3) (3x 1)(2x 2) 4) (x2
2)(x2 2)
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Unit 9 The Birthday Party Pinata

What did Lancelot Say to the Beautiful Ellen?
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Unit 9 The Birthday Party Pinata
CAPT Problems- Building a Cabin Grass Seed

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Unit 9 The Birthday Party Pinata

6 / Finish Work Sheet
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Unit 9 The Birthday Party Pinata Warm-up

Factor each of the following. 1) x2 x 6 2)
x2 7x 10 3) x2 16 4) 4x2 49
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Unit 9 The Birthday Party Pinata
BP-27 Jehrico is studying the expression 2(x
1)(2x 3) and is not sure where to start. He
thought he should first multiply 2 and (x 1),
and then multiply the result by 2x 3. But a
teamate told him to first multiply (x
1)(2x 3) and then multiply that result by 2.

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Unit 9 The Birthday Party Pinata
BP-27 2(x 1)(2x 3) a) Write down both
results. What do you notice? Find each of the
following products. b) 3(x 1)(5x 7) c) 5(x
3)(2x 5)

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Unit 9 The Birthday Party Pinata
BP-29 a) Make a table and draw the graph of y
x2 4. Mark and label the points where the graph
crosses the x-axis. b) Factor the expression x2
4 c) Substitute y 0 in the equation above to
get 0 x2 4. Use the Zero Product Property to
find the solution. What is the relation to part
a?

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Unit 9 The Birthday Party Pinata
BP-29 d) Solve x2 4 e) Solve x2 4 0 f) Did
you get the same results in parts (c), (d) and
(e)? What does this tell you about their graphs?
Explain.

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Unit 9 The Birthday Party Pinata
BP-39 Find the distance between each pair of
points. a) (5, -8) and (-3, 1) b) (0, -3) and (0,
5)

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Unit 9 The Birthday Party Pinata Quiz

BP-38 Bryce leaned his five foot rake against the
shed. The base of the rake was 2 fet from the
shed. How high up the shed did the tip of the
rake reach? Draw a right triangle diagram.
Write an equation and solve.
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Unit 9 The Birthday Party Pinata
BP-42 Solve each equation by factoring a) x2
13x 40 0 b) x2 15x 56 0 c) x2 144 0

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Unit 9 The Birthday Party Pinata
BP-40 Complete the following a) Add b) Solve

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Unit 9 The Birthday Party Pinata
BP-41 Solve for x and y 5x 2 y 3x y
-2

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Unit 9 The Birthday Party Pinata
BP-43 Find the slope and y-intercept of each
line, using any method you prefer. a) y (-2/3)x
1 b) y 5 (8/5)x c) 2x 3y 48

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Unit 9 The Birthday Party Pinata

5 / 310-311 / BP 33-35 312-313 / BP 44 45
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Unit 9 The Birthday Party Pinata
BP-28 A careless construction worker drove a
tractor into a telephone pole, cracking the pole.
The tope of the pole fell as if hinged at the
crack. The tip of the pole hit the level ground
24 feet from the base. The stump of the pole
stood 7 feet above the ground.

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Unit 9 The Birthday Party Pinata
BP-28 If an additional five feet of the pole
extends into the ground to anchor it, how long
should the replacement pole be? Draw a diagram.
Write an equation. Show all sub-problems as you
solve.

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Unit 9 The Birthday Party Pinata Warm-up
Complete the following a) b)

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Unit 9 The Birthday Party Pinata
BP-46 Fraction Busters the number we use to
eliminate the denominators. Example Solve

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Unit 9 The Birthday Party Pinata
BP-46 Solve The lowest common denominator is 15.

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Unit 9 The Birthday Party Pinata
BP-46 Solve

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Unit 9 The Birthday Party Pinata
BP-46 Solve Check
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Unit 9 The Birthday Party Pinata
BP-46 Solve
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Unit 9 The Birthday Party Pinata
BP-47 a) b) c) d)
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Unit 9 The Birthday Party Pinata
BP-48 The Buckled Railroad Track Railroad
designers are always looking for ways to improve
the safety and comfort of train travel.

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Unit 9 The Birthday Party Pinata
BP-49 A childs shoe box measures 4 x 6 x 3.
What is the longest pencil you could fit into the
box? An empty box may help you visualize the
varies ways you could fit the pencil in the box.
If possible, draw a diagram to show the pencils
position. Show your subproblems.

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Unit 9 The Birthday Party Pinata
BP-50 Solve for x. Use Fraction Busters. Leave
answers in Fraction Form. a) b) c) d)

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Unit 9 The Birthday Party Pinata
BP-51 Solve each of the following systems for x
and y. a) b)

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Unit 9 The Birthday Party Pinata
BP-52 Find the distance between each set of
points. a) (0, 5) and (5, 0) b) (-4, 7) and (29,
76)

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Unit 9 The Birthday Party Pinata
BP-53 Money Money Money Janelle has 20 and is
saving at the rate of 6 per week. Jeanne has
150 and is saving at a rate of 4 per week.
After how many weeks will each person have the
same amount of money. a) Make a graph to solve
the problem?

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Unit 9 The Birthday Party Pinata
BP-53 Money Money Money Janelle has 20 and is
saving at the rate of 6 per week. Jeanne has
150 and is saving at a rate of 4 per week.
After how many weeks will each person have the
same amount of money. b) Write equations to solve
the problem algebraically.

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Unit 9 The Birthday Party Pinata
BP-53 Money Money Money Janelle has 20 and is
saving at the rate of 6 per week. Jeanne has
150 and is saving at a rate of 4 per week.
After how many weeks will each person have the
same amount of money. c) Explain your solution
through your graph.

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Unit 9 The Birthday Party Pinata
BP-54 Solve each of the following equations by
factoring. a) g2 5g 6 0 b) m2 5m 6
0 c) e2 10e 21 0 d) h2 16h 36 0

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Unit 9 The Birthday Party Pinata
BP-55 Graph using the slope and
y-intercept. a) b)

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Unit 9 The Birthday Party Pinata

8 / BP 52, 53, 54, 55
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Unit 9 The Birthday Party Pinata Warm-up
Factor each expression. 1) 2) 3) 4) 5)
6)

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Unit 9 The Birthday Party Pinata
BP-57 Use your calculator to determine which of
the following statements containing unlike square
roots are true and which are false. a)
b) c) d)

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Unit 9 The Birthday Party Pinata
BP-58 a) Which kinds of square root operations in
BP-57 were true? b) Which kinds of square root
operations in BP-57 were false? c) Write
conjectures about using the different operations
(, -, , /) with unlike square roots. (TOOL
KITS!)

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Unit 9 The Birthday Party Pinata
BP-59 - Use your conjectures to simplify these
expressions as much as possible. Do not leave
perfect squares. a) b) c) d) e) f)

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Unit 9 The Birthday Party Pinata
BP-60 Graphing Square Roots a) Graph on
your resource page. b) What values are possible
in part (a)? c) Compare this graph to BP-15 and
BP-44 (They are on your resource page.

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Unit 9 The Birthday Party Pinata

9 / BP 63, 64, 66, 67, 68
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Unit 9 The Birthday Party Pinata Warm-up
Solve each quadratic. 1) 2) 3)
4) 5) 6)

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Unit 9 The Birthday Party Pinata
Simplifying Square Roots -Simplify 1) Construct a
factor tree

3, 3, 5 are the prime factors of 45
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Unit 9 The Birthday Party Pinata
-Simplify 2) Make groups of two with the prime
factors.

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Unit 9 The Birthday Party Pinata
-Simplify 3) Rewrite the prime factors under the
radical, multiply the group of two, leave the
other number the way that it is.

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Unit 9 The Birthday Party Pinata
-Simplify 3) Separate the radicals into two
radicals multiplied together.

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Unit 9 The Birthday Party Pinata
-Simplify 4) Take the square root of the perfect
square, leave the other square root alone.

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Unit 9 The Birthday Party Pinata
-Simplify the following radicals. 1) 2)

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Unit 9 The Birthday Party Pinata
BP-71 Consider each factored choice below, then
write the square root in simplified form. a) To
simplify , would you factor it into or
Why? b) To simplify , would you factor it
into or Why?

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Unit 9 The Birthday Party Pinata
BP-72 Write the following square roots in
simplest form a) b) c) d) e) f)

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Unit 9 The Birthday Party Pinata

10 / Finish WS, BP 73, 76, 77
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Unit 9 The Birthday Party Pinata Warm-up
There were 16 schools at the regional swim meet.
An average of 14 swimmers were on each school
team. How many swimmers were at the swim
meet? -Show all of your work, and explain how you
arrived at your answer.

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Unit 9 The Birthday Party Pinata
BP-76 Graphing Square Roots. Use your
calculator to graph on your
resource page from BP-15 a) What happened if you
use x -3 in the square root? b) What values are
possible for x?

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Unit 9 The Birthday Party Pinata
BP-77 Graphing Square Roots. Use your
calculator to graph
on your resource page from
BP-15 a) What happened if you use x -1 in the
square root? b) What values are possible for x?

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Unit 9 The Birthday Party Pinata
BP-77 Graphing Square Roots. Use your
calculator to graph
on your resource page from
BP-15 c) Compare this graph to that of BP-15.
What is the effect of adding a number to a
graph?

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Unit 9 The Birthday Party Pinata
BP-77 Graphing Square Roots. Use your
calculator to graph
on your resource page from
BP-15 d) How are the equation and the graph
different from BP-44

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Unit 9 The Birthday Party Pinata
BP-78 Factor each of the following
expressions. a) b) c)

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Unit 9 The Birthday Party Pinata

11 / Finish WS, BP 79, 80, 81, 82
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Unit 9 The Birthday Party Pinata Warm-up
One coach wanted her team to swim 16 laps to warm
up before the races started. To complete each
lap, they had to swim to the end of the pool and
back. The pool was 25 meters long. How far did
they swim? -Show all of your work, and explain
how you arrived at your answer.

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Unit 9 The Birthday Party Pinata
BP-74 Draw a sketch of two line segments which
have the same slope but which are not part of the
same line. What one word best describes the
relationship of the two line segments?

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Unit 9 The Birthday Party Pinata
BP-75 Find the equations of the lines graphed on
the board.

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Unit 9 The Birthday Party Pinata
How to find the equation of the line without
graphing. Ex Find the equation of the line
passing through (3, 4) and (4, 6) 1) Write the
general equation of a line. y mx b

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Unit 9 The Birthday Party Pinata
Ex Find the equation of the line passing through
(3, 4) and (4, 6) 2) Calculate the slope by
drawing a generic slope triangle.

1
m 2/1 2 So, the equation of the line is
y 2x b
(4,6)
2
(3,4)
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Unit 9 The Birthday Party Pinata
Ex Find the equation of the line passing through
(3, 4) and (4, 6) 3) Find the y-intercept, b,
without a graph. Remember, we know that (3, 4)
is on the line. This means that we can substitute
(3, 4) for (x, y) in the equation and solve for
b. y 2x b

4 2(3) b
-2 b
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Unit 9 The Birthday Party Pinata
Ex Find the equation of the line passing through
(3, 4) and (4, 6) 4) Finally write the equation
of the line with the slope and the
y-intercept. y 2x 2

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Unit 9 The Birthday Party Pinata
BP-84 Find the equation of the line passing
through each pair of points. Be sure to show all
of your work. (y mx b) a) (4, 6) and (6,
7) b) (9, 8) and (3, 5) c) (-3, 2) and (4, 5)

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Unit 9 The Birthday Party Pinata
BP-85 a) A certain line with slope 1 / 2 goes
through the point (6, 1). Find the equation of
the line in the form of y mx b. b) Suppose
the line y 2x b goes through the point (1,
4). Find the equation of the line.

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Unit 9 The Birthday Party Pinata
BP-86 Explain to a student who was absent how you
would find an equation of a line through two
given points. Please write on a separate sheet
of paper. Write your answer in complete
sentences. (Reflection)

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Unit 9 The Birthday Party Pinata

12 / Finish WS, BP 99, 103, 104
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Unit 9 The Birthday Party Pinata Warm-up
Jessie finished the first race in 2 minutes 7
seconds. Tim finished 12 seconds faster than
Jessie. Juan finished 8 seconds faster than Tim.
How long did it take Juan to finish? -Show all of
your work, and explain how you arrived at your
answer.

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Unit 9 The Birthday Party Pinata
F.O.I.L. In multiplying binomials, such as (3x
2)(4x 5), you might use a generic
rectangle. Another approach to multiplying
binomials is to use the mnemonic F.O.I.L. It is
an acronym for First, Outside, Inside, and Last.

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Unit 9 The Birthday Party Pinata
F.O.I.L. (3x 2)(4x 5) F. Multiply the FIRST
terms of each binomial. (3x)(4x) 12x2 O.
Multiply the OUTSIDE terms. (3x)(5) 15x I.
Multiply the INSIDE terms.
(-2)(4x) -8x L. Multiply the LAST terms.
(-2)(5) -10

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Unit 9 The Birthday Party Pinata
F.O.I.L. (3x 2)(4x 5) Finally we combine
like terms 12x2 15x 8x 10 12x2 7x 10

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Unit 9 The Birthday Party Pinata
BP-91 Multiply these binomials. Check your
work. a) (7x 4)(3x 2) b) (9x 7)(4x 3) c)
(2x 5)(3x 10) d) (5x 4)(3x 2) e) (x
4)(x2 5x 7)

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Unit 9 The Birthday Party Pinata
BP-92 a) John Bluecloud builds four square pens
(each equal area) side by side in a row. He uses
83.2 feet of fencing material. What are the
dimensions of each pen? b) John figures he can
make each pen larger if he places the squares in
a square pattern. Is he right? Explain.

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Unit 9 The Birthday Party Pinata
BP-93 The top of Susans telephone table is a
semi-circle (half of a circle). Its diameter,
against the wall, is 2.5 feet. Find the area of
its top surface.

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Unit 9 The Birthday Party Pinata

13 / BP-95 (Project Grade)
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Unit 9 The Birthday Party Pinata Warm-up
Worksheet on Front Desk. -Show all of your work,
and explain how you arrived at your answer.

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Unit 9 The Birthday Party Pinata
Laws for Square Roots for Positive s

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Unit 9 The Birthday Party Pinata
BP-102 A young redwood tree in Muir Woods casts a
shadow 12 feet long. At the same time, a five
foot tall tourist casts a shadow two feet long.
How tall is the tree? Draw a diagram, use ratios
to write an equation, and then solve the equation.

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Unit 9 The Birthday Party Pinata
BP-105 Solve each of the following equations
for x. a) x2 140 4 b) x(x 1)(x 2)
0 c) d) 2x 3y 5

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Unit 9 The Birthday Party Pinata
BP-109 Find the length of the diagonal of a
square whose sides have length 5 inches. Sketch a
diagram and solve.

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Unit 9 The Birthday Party Pinata
BP-110 Janis is going to fence off a rectangular
garden. She will use an existing wall along the
back, and she wants the length to be twice as
long as the width. The total amount of fencing
material she has is 84 meters long. What are the
width and length of her garden. Draw a diagram,
write an equation and solve.

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Unit 9 The Birthday Party Pinata

14 / BP-111, 112, 113,114, 115,116