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Holt Modern Chemistry Review
CHAPTER 11: GASES
The following pages contain the bulk (but not all) of the information for the chapter 11 test.
Focus on this content, but make sure to review class notes, activities, handouts, questions, etc.
If you study this document and NOTHING else, you should at least be able to PASS the test.
***** Test items will be recall, examples, and/or application of this content. *****
Economics Chapter 6: Markets, Maximizers, and Efficiency
Start Up: A Drive in the Country
Suppose you decide to take a drive. For purposes in this example, we?ll assume that you have a car, that the weather is nice, and there?s an area nearby that?ll be perfect for the drive.
Your decision to take a drive is a choice. Since economics deal w/ choices, we can put econ. To work in thinking about it. Economists assume that people make choices that maxes utility
Utility is the satisfaction you gain from your use of goods/services and from activities you do
Economics Chapter 5, Elasticity: A Measure of Response Notes
Section 4-6: The Quadratic Formula and the Discriminant
The standard form of a quadratic is: +(''
The quadratic formula is: )(. - - , where a, b, and c are real
numbers where a # 0. -
> What is the purpose of using the quadratic formula?
:
/
What is the expression used to find the discriminant: \
> What information does the discriminant tell you? / (IC IS
Value of Discriminant: (
Number and types of
'I \ (
solutions:
Graph will look like:
Ex 2: f(x)= 7x2 +28x+56
o X1-F4(tsl'
-
-
? 510 71-J
2 +q)c
-- (9'' H
84- x L +Lfx+ i
F-4 = F( T *?g J?Z
t r?q
-
= )C+z
H
Fx ?2? j
Section 4-5: Solving with Completing the Square
The Process
1) Set equation 0
2) Shove the constants to the other side
3) Get the Leading Coefficient to be 1
4) Complete the Square. Then add that
value to both sides.
5) Take the square root of both sides and
solve for x.
Section 4.5: Vertex form with Completing the Square
Completing the Square: Used to change quadratic functions in standard form to vertex form.
f (x) = ax 2 + bx + c - f(x)=a(x?h) 2 +k
------------------------
Investigation This creates a
Perfect Square
2 (b)2 Tririomiai, which factors To complete the square for an expression x + bx, add
------
Startwithx2
+ bx Find
(b)2 x2 +bx+() (x+ )2 /
The Completed Square Factored form
x2 +6x -
x2 +4x
2 X - 8x
_)
-
3
H
5
Vt4Section 4.7: Graph of Quadratic Functions in Vertex or Intercept rm.
J
*Reca ll the transformations from Section 2.7 we learned f(x) = a I x
- hi + Ic for absolute value functions.
Vertex Form of a Quadratic f(x) =' (x - h)2
+
? Vertex: -Kit itc'1eS-- 0 r
2f4oO&1
Axis of Symmetry:
In 0
*l.L
tot,&) J'&H- ? Opens up/down if:
Example 1: Given f(x) = x2, write it in vertex form and graph.
totAJe-k- polv1+ on
?6= ?2
b) 25 c) 7(x-4)2 ?18=10
tt fS
)c 100
-
f(TI1)jii
Solving Quadratic Equations by Finding Square Roots
Objective: To solve quadratic equations with real solutions.
If R2=S, then Risa (00+ of S.
A positive number S has 2 square roots written as ( and . ?O
Properties:
Product Property: V'-a-
Quotient Property:Tb
Simplify the expression (radical)
a) b) c) id * 1-5
Rationalize Denominators of fractions 1 1 5D re: a, /
1,0
a)
J ~S? I-
b)
Section 4.3: Solve by Factoring
Vocabulary
? Monomial: OA 4?ct&in j?W
? Binomial: cuij e'ICS 1uX i-ewis
Trinomial: CLAA Cc(.1 tJ9 :!2i *ermS
*Some binomials and trinomials will have a Greatest Common Factor (GCF) that we will factor ou7
when factoring
? Solutions to a Quadratic Equation: X-'zef1 (O*5
so W )(-V 0
Greatest Common Factoring
Ex1: Factor 3x2 +9x QCF? Ex 2: Factor 4x + 6
..
Name: Date:
Section 4-2 Notes
Graphing Quadratic Functions in ird For
Standard form of a quadratic function is E ax - A
The parent function of the family of all quadratic functions is f(x)
The graph of a quadratic function is a DaYWO01 IA.
The vertex of a parabola is the or point on the
parabola.
.-.J
00
The axis of
jcnY1LeA-rJ7 divides the parabola into mirror images and passes through the
Graph the function y = CoWare to Graph the function y = (_--x)2. Compare it to
Section 2-1: Relations and Functions
Goal: Write the domain and range of afunction in interval notation, inequalities, and set notation.
? Domain (Independent variable, InputvaIue,x)? ?- Of 4) OO't t
'? x: (iI)(3)(5
? Range (dependent variable, output value, y)? ?* oj,,l L4- 00r7J1
4i V' x: (t, I) (3,)?, )
? Set Notation? ?TE 4 f
-
s c coIIeq, o ,ftM~,
? Relation?
k 4 &QA
"V
? Vertical Line Test?
Function-
L i\
ecA'l xqvf
&9rn-M (c) I Cam
Pages
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