Unit 10 Yearbook Sales

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Unit 10 Yearbook Sales 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
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 10 Yearbook Sales
YS-11 Multiply each of the following binomials
a) (x 1)(x 1)
b) (x 5)(x 2)
c) 2x(x 5)
d) (2x 1)(x 5)
e) (x y)(x y)
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Unit 9 The Birthday Party Pinata
Laws for Square Roots for Positive s

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Unit 10 Yearbook Sales
YS-1 Tool Kit Factoring when a 1 Example
2x2 7x 3
multiply
6
6
2x2
6x
?
?
1
6
3
1x
7
7
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Unit 10 Yearbook Sales
YS-1 Example 2x2 7x 3
x
3
2x
2x2
6x
2x2
6x
(2x 1) (x 3)
3
1x
1x
3
1
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Unit 10 Yearbook Sales
YS-2 Factor each of the following quadratics
using the modified diamond procedure. a) 3x2 7x
2
b) 3x2 x 2
d) x2 4x 45
c) 2x2 3x 5
e) 5x2 13x 6
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Unit 10 Yearbook Sales
YS-3 Factor each of the following quadratics.
a) 3x2 9x 30
b) 5x2 20
c) 4x2 4
d) 3x2 11x 6
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Unit 10 Yearbook Sales
YS-4 Use the Zero Product Property to solve
each quadratic equation. a) (x 2)(x 7) 0
b) (2x 1)(x 5) 0
c) x2 3x 10 0
d) y2 7y 10 0
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Unit 10 Yearbook Sales
YS-5 Factor each of these quadratics. a)15x2
37x 18
b) 42x2 17x 15
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Unit 10 Yearbook Sales Warm-up
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Unit 10 Yearbook Sales
YS-14 Solve each of the following equations or
systems by any method your choose. Show all of
your work. a) x2 10x 21 0
b)
c) 2x2 7x 15 0
d)
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Unit 10 Yearbook Sales
YS-14 Solve each of the following equations or
systems by any method your choose. Show all of
your work.
e) x 2y 1
f) x2 5x 24
y x -5
g) 2(x 1) 4(x 2) x 3
h) y -x 2
y 0.5x 4
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Unit 10 Yearbook Sales
YS-16 Graph the following 3 lines. Use
sub-problems and systems of equations to answer
the following questions.
a) Where do the lines intersect? b) Find the area
of the triangular region formed by the three
equations.
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Unit 10 Yearbook Sales
YS-12 Factor each of the following quadratics,
if possible. a) x2 3x 10
b) y2 7y 10
d) 2y2 11y 21
c) x2 3x 10
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Unit 10 Yearbook Sales
YS-13 Factor each of the following quadratics
completely. Then check your answer. a) x2 10x
21
b) 3x2 7x 2
d) x2 64
c) 2x2 7x 15
f) x2 14x 49
e) 6x2 2x 48
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Unit 10 Yearbook Sales
YS-17 Factor each of the following quadratics
by looking for common factors.
a) x(x 2) 3(x 2)
b) 2y(y 3) 5(y 3)
c) (x 4)x2 3(x 4)
d) (y 1)2 (y 1)
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Unit 10 Yearbook Sales Warm-up

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Unit 10 Yearbook Sales
YS-23 Complete the following.
a) Factor 3x2 5x 2
b) Solve 3x2 5x 2
c) What do your answers in part (b) tell you
about the graph of y 3x2 5x
2?
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Unit 10 Yearbook Sales
YS-25 Write each of these expressions as simply
as possible using the method shown below.
Knowing that x3 x x x and
then x(x3) x (x x x) x4
and
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Unit 10 Yearbook Sales
YS-25 Simplify the following
a) x2 x
b) y2 y5
c) x3 x6
d)
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Unit 10 Yearbook Sales
YS-26 Put in your Tool Kits!! Base,
Exponent, and Value In the expression 25, 2 is
the base, 5 is the exponent, and the value is
32. 25 means 2 2 2 2 2 32 x3 means
x x x
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Unit 10 Yearbook Sales
YS-27 Use exponents to write each of the
following expressions as simply as possible.
a) (x2)(x5)
f) x3 x4
g) m13 m14
b) x7 x5
h) x32 x59
c) y8 y6
d) y7 / y4
i) x31 / x29
e) x3 / x1
j) x3 / x3
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Unit 10 Yearbook Sales
YS-28 Put in Tool Kits!! Write the meaning of
each then simplify using exponents. EXAMPLE
(x3)2 x3 x3

(x x x)(x x x) x6
d) (x y)2
a) (x4)2
b) (y2)3
e) (x2 y3)3
c) (x5)5
f) (2x)4
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Unit 10 Yearbook Sales
YS-29 Using the patterns for the exponents that
you have found, write each expression below as
simply as possible using exponents.

d) (xy2)2
a) x3 x4
e) (2x2)3
b) (x3)4
f) (x2y2)4
c) x4 / x5
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Unit 10 Yearbook Sales
YS-30 Use your calculator to write these
exponential numbers as a decimal and as a
fraction.
a) 10-1
b) 100
c) 5-1
d) 5-2
e) What effect does a negative sign have when it
appears in an exponent? Was this what you
expected?
f) What effect does zero have when it appears as
an exponent?
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Unit 10 Yearbook Sales
YS-31 Use the modified Diamond method from YS-1
to factor.
a) 6x2 5x 1
b) 4x2 4x 1
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Unit 10 Yearbook Sales
YS-38 Summarize the patters that you found in
the exponent problems. Describe how to write the
examples below as simply as possible.

What patterns did you find? Use the words base
and exponent.
a) (x2)(x3)
b) x6 / x3
c) (x3)4
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Unit 10 Yearbook Sales
YS-39 Use the patterns that you described in
the previous problems to write each expression as
simply as possible.

a) (x7)(x4)
e) (2x2)3
b) (x3)3
f) (x2y2)4
c) x6 / x3
g)
d) 86 / 83
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Unit 10 Yearbook Sales
YS-40 TOOL KITS!!! Laws of Exponents 1) xa
xb xa b Ex x3 x4 x3 4 x7 2) xa / xb
xa b Ex x10 / x4 x10 4 x6 3) (xa)b
xab Ex (x4)3 x4 3 x12
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Unit 10 Yearbook Sales
YS-43 TOOL KITS!!! Zero Exponents Negative
Exponents 1) x0 1 Ex 20 1 2)
x-n 1 / xn Ex x-3 1 / x3 3) 1 / x-n xn
Ex 1 / x-5 x-5
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Unit 10 Yearbook Sales - Quiz
Simplify the following expressions 1) y6y3 2)
(m6)3 3) (3a)5 4) x9 / x2 5) (12x10) /
(4x3) 6) (y5)2 7) x3 x4 8) (x5)2
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Unit 10 Yearbook Sales Warm up
Investigate the following problems using a
calculator. 1) Is 2) Is 3) Is 4) Is
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Unit 10 Yearbook Sales
Reflecting on your warm-up. What is the only
mathematical operation that allowed us to write
the same factor in the numerator and denominator
as ONE? SO Which one is true? a) b)
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Unit 10 Yearbook Sales
TOOL KITS!! Simplifying Rational Expressions To
simplify rational expressions, both the numerator
and denominator must be factored, Then look for
factors that make ONE (1). Ex
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Unit 10 Yearbook Sales
YS-64 Simplify each rational expression. a) b)
c) d)
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Unit 10 Yearbook Sales
TOOL KITS! Standard Form of the Quadratic
Equation ax2 bx c 0 2x2 13x 21
0 a 2 b -13 c 21
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Unit 10 Yearbook Sales
YS-76 Identify the values of a, b, and c in
each of the following quadratic equations. a) 3x2
5x 4 0 b) x2 9x 1 0 c) -2x2 9x
0 d) -6x 5x2 8 e) 0.017x2 0.4x 20
0 f) x(2x 4) 7x 5
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Unit 10 Yearbook Sales
TOOL KITS!! Quadratic Formula If ax2 bx c 0
then
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Unit 10 Yearbook Sales
Remember means that there are two solutions.
and
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Unit 10 Yearbook Sales
Steps for using the Quadratic Formula 1) Put the
equation in standard form 2) List the numerical
values for a, b, and c 3) Write the Quadratic
Formula 4) Substitute the numerical values for a,
b, and c in the Quadratic Formula
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Unit 10 Yearbook Sales
Steps for using the Quadratic Formula 5)
Simplify to get the exact solutions. 6) Use a
calculator, if necessary, to get approximate
solutions.
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Unit 10 Yearbook Sales
YS-87 Solve using the Quadratic Formula x2 2x
4 1) x2 2x 4 0 2) a 1 b -2 c
-4 3)
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Unit 10 Yearbook Sales
YS-87 Solve using the Quadratic Formula x2 2x
4 4) 5)
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Unit 10 Yearbook Sales
YS-87 Solve using the Quadratic Formula x2 2x
4 6) x 3.24 x -1.24
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Unit 10 Yearbook Sales
YS-88 Solve using the Quadratic Formula a) 2x2
9x 35 0 b) 3x2 7x -2 c) x2 5x 2
0 d) 8x2 10x 3 0
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Unit 10 Yearbook Sales
YS-95 Solve using the Quadratic Formula a) -4x2
8x 3 0 b) -3x -x2 14 c) -5 11x
2x2 d) 0.09x2 0.86x 2 0 e) 3x2 4x 0
f) 25x2 49 0 g) Which of these equations
could you have solved by factoring?
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Unit 10 Yearbook Sales
YS-96 Refer to YS-95 to answer the
following. a) List the values of for each
part of YS-95. b) Find the equations that had
rational numbers (integers or fractions) for
their solutions. Compare the values of
for these equations to the values of for
the equations whose solutions were not integers
or fractions. What do you notice?