Algebra 2: Topic Outline
I. Intro to Functions unit
1. Function basics
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Function concept and f(x) notation
Ways to represent or describe functions: formula, table, graph, verbal
Finding an output given an input, or an input given an output
Deciding whether a table/graph shows a function or not
Identifying domain and range
Concept of zeros
2. Graphing calculator use, including intersections, zeros, maximum and minimum
3. Solving equations
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Solving equations with linear functions algebraically
Solving equations using the intersection of two graphs on your calculator
4. Solving inequalities graphically and algebraically
5. Composite and inverse functions
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Given two functions f(x) and g(x) as formulas, tables, or graphs, finding and using the
composite function g(f(x))
Using various meanings of the concept that two functions are inverses of each other
Given a function f(x), finding its inverse f –1(x) using tables (reverse columns),
graphs (reverse coordinates), or formulas (“change and solve”)
II. Linear functions
y 2 - y1
or a table or a graph
x 2 - x1
Point-slope form f(x) = m(x – h) + k
Slope-intercept form f(x) = mx + b
Finding the slope using m =
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Graphs of linear functions
Graphing point-slope lines, using a starting point and the slope
Horizontal lines (y = #) and vertical lines (x = #)
Parallel lines (equal slopes) and perpendicular lines (opposite reciprocal slopes)
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Evaluating and solving
Given an input, finding an output (evaluating)
Given an output, finding an input (solving equations)
Solving inequalities and double inequalities
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Finding composite functions and inverse functions
Modeling (application) problems
Meaning of slope: a rate or a speed
Turning word problems into function formulas
Domain and range
Evaluating/solving (see above) and giving the meaning of the answer in the problem context
III. Logs and exponents
Basic properties of exponents
Use of negative and fractional exponents
Simplifying and rewriting expressions using exponent properties. Combining like terms, but not
combining unlike terms.
 Logarithms
Solving bx = c using x = logb c; on calculator: LOG(c)/LOG(b)
Finding values of logs by interpreting them as questions
Converting between exponential and logarithmic equations
 Exponential functions
 Exponential modeling (application problems)
Setting up an exponential function using a starting value and a multiplier
Answering input-output questions (evaluating and solving).
IV. Quadratic Functions:
1. Three forms
a. Standard Form: f (x)  ax 2  bx  c
b. Factored Form: f ( x ) = a( x - b)( x - c )
c. Vertex Form: f ( x ) = a( x - h) + k
You need 
to be able to transform functions from one form to another. The skills you
need to do this are 1) factoring, 2) multiplying, and 3) completing the square,
2
2. Properties of quadratic functions
a. Zeros: find them by: 1) factoring, 2) taking square roots (if appropriate) or 3) using
the quadratic formula.
b. Vertex: Three ways to find the x coordinate: average the zeros for factored form,
b
use x 
for standard form and just look at the equation for vertex form. Once
2a
you find x, plug in to find y. In the calculator section of the test, you can find the
vertex by finding the maximum or minimum using the 2nd Trace command.
c. End behavior
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3. Graphing a quadratic function in vertex form and factored form.
4. Writing a formula for a quadratic function given a graph. Use either factored form or
vertex form depending on the information you are given.
5. Solving quadratic equations. (“Find the value(s) of x that make the equation true.”)
6. Quadratic application problems (projectiles).
V. Polynomials:
1. Graph a polynomial function in factored form. To do this you need to know:
a. End behavior
b. Zeros and multiplicity
c. Y-intercept
2. Factoring a cubic equation:
3. Write a polynomial function from a graph when you know the shape and some points.
4. Dividing polynomials using long division
VI. Systems and Matrices
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Solving linear systems by substitution and elimination methods (only for 2 equations, 2
variables)
 Solving linear systems by matrix elimination method
Doing row operations by yourself
Getting the reduced matrix from calculator rref command
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Recognizing whether a system has one solution, no solutions, or infinitely many solutions
Word problems involving linear systems
VII. Counting and Probability
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Probabilities in situations where the outcomes are equally likely.
Probability of a single outcome =
Probability of an event =
1
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total number of outcomes
number of outcomes in the event
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total number of outcomes
Using counting methods (such as C, P, or !) to find “the total number of outcomes” and/or “the
number of outcomes in the event.”
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Probabilities involving “and”, “or”, “not”
(here A and B stand for events)
P(not A) = 1 – P(A)
P(A or B) = P(A) + P(B) – P(A and B)
P(A or B) = P(A) + P(B) if A and B are mutually exclusive because then P(A and B) = 0
Venn diagrams.
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Dependent and independent events
If events A and B are dependent (the outcome of A affects the likelihood of B):
P(A and B) = P(A) · P(B | A)
where P(B | A) means prob. of B given A
If events A and B are independent:
P(A and B) = P(A) · P(B)
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Repeated binomial experiments: For an action having two equally-likely outcomes (such as a
C
coin flip) done n times, the probability of getting a certain outcome r-out-of-n times is n n r
2
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Expected value (multiply each outcome times its probability, then add)
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Conditional probability in tree diagrams and in tables