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Graphing Quadratic Functions
The parent function
Use a table to plot points and graph:
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! = x2. Show your work here:
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use your calculator to graph the following equation in the same window:
Show your graphs here. Draw the graphs accurately, being especially careful to get the right values at
1 andx: -1.
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Polynomial in one variable: A polynomial degree n in one variable x is an expression where the numbers in front
of the variables are integers. Ex) 3xa + 4x3 - 6xz + 4x - 7
7-7 Operations of Functions
Algebra of Functions: Finding the sum, difference, product, and quotient of functions to
Lf +sxx) = f (x)+ g(x)
7-8 Inverse Functions
Two relations are inverse relations if and only if whenever on relation contains
the element (a,b)" the other relation contains the element (b,a)
uare Root Functions and In
A function that contains the square root of a variable expression.
Like parabolas (quadratic functions), square root functions can be graphed
+ k , where a:vertical stre
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Chapter 6 Review
12. The quadratic equation xz + &: 1 is to be solved by completing the square'
Which equation would be the first step in tlat solution?
6.3 Factoring Review
Example) Factor 4-term polynomials by grouping.
1. Factor out GCF
2. Group into two groups.
3. Find GCF of each gr
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6.4 Completing the Square
Property I Fo, ury real number x, ifx2 = n , thenx = +Ji
Example) Solve each equation by using the square root property.
a) x2 -8x+16=25
1. Rewrite polynomial in pe
5-6 Radical Expressions
Objective 1: Use the product rule for radicals.
Product Rule for Radicals: lf qfa and tl6 are rea] numbers, then cfw_a . lt6
To simplify a square root, follow these steps:
1. Factor the radicand into as many squares as possible.
5-7 Rational Exponents
Objective 1: Understand the meaning ol a* .
Definition: lf r is a positive integer greater than 1 and da is a real number, lhen da : a*
the denominator of the rational exponent corresponds to the index of the radical.
5-8 Radical Equations
Objective 1: Solve equations that contain radical expressions.
Solving a Radical Expression
Step 1: isolate one radical on one side of the equation.
Step 2: Raise each side of the equation to a power that will eliminate the radical a
5-9 Complex Numbers
Objective 1: Define imaginary and complex numbers.
lmaginary unit: i L 1:7
. Ja i,la
Example 1: Write with i notation.
Example 2: Multiply or divide as indicated.
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2.1 Graphing Equations
Objective 1: Plot ordered pairs.
Cartesian coordinate system (rectangular coordinate system) is a grid used to locate points on a plane.
The horizontal axis is called the x-axis, and the vertical ax
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Algebra ll CRT Review
Solving Systems of Equations
1. Graph the equations
2. Find the point where the two graphs intersect.
3. The ordered pair for point is your solution. (x,y)
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2.2 tntroduction to Functions
Objective 1: Define relation, domain, and range
Relation - set of ordered pairs. .r corresponds toy ory depends on x.
A map illustrates a relation by using a set of inputs and drawing arro
12-2 Per.tnutations and Cornbinations
Permutations: When a group of objects or people are arranged in a certain order, the
arrangement is called a pemutation.
Permutations - The number of permutations of n distinct objects taken r at a time is given
Block 4 Assessment - Quadratics
Quadratic Equations are in the form
axz + bx + c and form a u-shaped graph.
When graphing quadratics you can find the following:
1. x-intercepts (roots or solutions of the equation)
2. vertex (place where the graph f
Determine which of the graphs shown here
could be used to solve this equation: \.
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10.2 Logarithms and Logarithmic Functions
The logarithm of x with base b is defined as:
logrx=y e x=bY
Where r)0, b>0,andb*l
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b) logr16=1 g3,
10.3 Properties of Logarithms
Properties of exponents can be used to develop the following properties of logarithms.
(Remember a logarithm is an exponent)
Product Property of
MN = log, M +logu N
M, N, b, andP are positive real numb
10.4 Common Logarithms
10,5 Natural Logarithms
Use a calculator to evaluqte each expression to four decimal places.
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10.6 Exponential Growth and Decay
When a quantity increases by a fixed percent each time period, the amount of that
quantity after t time periods is given by
y = a(1+ r)'
a: initial amount
r : percent increase (or rate of g