# Algebra 2 Final Basic Study Guide (read description)

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Velocity Problems Formula

FEET PER SECOND=Height(H)= velocity(v) x Time(T) – 16 x (T squared) METERS PER SECOND= Height(h)=velocity(v) x Time(T) -4.9 x (T squared)
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Quadratic Formula (This was mostly covered semester 1, but it’s almost always applicable in algebra so you should definitely still know it). Btw remember that variables nect to each other mean multiplied (I had to do this a little with this formula to format it correctly).

x = -b ± (√b² – 4ac) ÷ 2a
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Standard Quadratic Form (this is when you would use quadratic formula, so you should be able to recognize this)

ax² + bx + c = 0
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y = a(x-h)² + K If a>0 then the parabola opens up with minimum vertex. If a<0 then parabola opens down with maximum vertex Vertex will always be (h,k), note that it is ALWAYS a positive \"h\" Axis of symmetry will always be x=h, again note the positive \"h\"
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Standard Form

y = ax² + bx + c
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To find vertex from standard form

(-b ÷ 2a, plug x coordinate in and solve for y) In standard form y intercept is always (0,c)
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Discriminant

b² – 4ac If discrimant0 then zeros will be real numbers, 2 x intercepts. If discriminant=0 then one zero, and will be real number. x intercept=vertex. If positive and perfect square it will be rational If positive but not perfect square it will be irrational.
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Degree

The greatest exponent of a polynomial’s terms. If the polynomial has more than one variable you need to add the exponents in each term, the greatest value of these sums is the degree.
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Polynomial Expression

Where the degree of each term is a whole number.
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The constant of the term with the highest degree.
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Multiplication rule for monomials

a(to the power of m) x a(to the power of n) = a(to the power of m +n)
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List of ways to factor

1. GCF 2. Special Case a.Difference of 2 squares b. Sum/Difference of 2 cubes 3. 2 binomials 4. Grouping
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Dividing variables

You subtract the exponents Example: x³ ÷ × = x²
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Rules for when synthetic division works

1. Divisor is linear (no exponents in bottom) 2. Have to be able to put divisor in \”x-a\” form How to set it up: a| coefficients of dividends in descending order Example: (x² – x – 6) ÷ (x – 3) 3| 1 -1 -6 ↓ ↓ ↓ + 0 3 6 ———————— 1 2 0 first degree coefficient, constant, remainder.
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Rational Root Theorem

Tells possible rational roots (solutions effectively). Once you find one that works via synthetic division you just have to factor to find all answers. P (Factors of Constant) ÷ Q (Factors of Lead Coefficient)
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Sum/Product of Quadratic Roots Btw personally I didn’t understand this totally, but there’s a good youtube video to explain it (first one when you look it up)

Sum = -b ÷ a Product = c ÷ a Basically, when condense everything down you can solve quadratic equations by utilizing this concept like this: a² + (-sum of roots) + (product of roots) It’s actually very useful, and can be used in place of the quadratic formula.
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Division Rule for Monomials

x(to the power of m) ÷ x(to the power of n = x(to the power of m-n)
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Power Rule

(a to the power of m)(raised to the power of n) = a( to the power of m x n) Example: (x²)³ = x⁶
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Power of a Product

(a x b)(to the power of m) = a(to the power of m) x b(to the power of n)
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Power of a Quotient

(x÷y)(to the power of m)= x(to the power of m) ÷ y(to the power of m)
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Zero Power

x⁰ ALWAYS = 1
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Negative Power

x⁻¹ = 1 ÷ x
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You can only add if radicals/exponents are the same. Remember that you can never have radical in denominator.
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Solving Equations with Radicals

1. Isolate radical. 2. Square/cube/etc. to eliminate radical 3. Solve 4. Check. or 1. Isolate radical 2. Raise to power of reciprocal. 3. Solve 4. Check.
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Variables as exponents

Make coefficients the same and set exponents equal to each other.
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Interest Problems

Formulas: Simple: Principal x Rate = Interest Compound: Balance = Principal(1 + interest rate ÷ number of times per year compounded)(to the power of number of times per year compounded x time in years) Continuously compounding: P x e(to the rate of growth/decay percentage x time in years)
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Common logarithm

Base 10.
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Natural Logarithm

Base \”e\”.
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Matrices Basic Information

How do you name a matrix? Name it a variable. Dimensions of a matrix? # of rows by # of columns. Types of matrices? 1. Square Matrix- # of roms = # of columns. 2. Row Matrix- 1 row. 3. Column Matrix- 1 column. 4. Zero Matrix- All entries are 0. 5. Identity Matrix- All entries are zero except diagonal 1’s.
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Adding and Subtracting Matrices

1. Dimensions must match. 2. Add of subtract corresponding entries.
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Multiplying Matrices (by other matrices not scalar)

1. Inner Dimensions must match. 2. Outer dimensions will tell dimensions of product.
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Determinants

Shown by: | a b| (lines would be connected however) |c d| Criss cross multiply and subtract bottom minus top (ad-bc) With non-square matrices you rewrite the first two columns to side, criss-cross multiply and add, and subtract bottom minus top. |a b c d| a b |e f g h | e f |i g k z| i g
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Cramer’s Rule

This is based off of this format: Coefficient matrix x variable matrix = constant matrix Denominator of x answer is always the determinant of coefficient while for the numerator you sub in constants for x column and find discriminant. For y denominator is also determinant of coefficient and numerator is determinant of coefficient with constants in y column.
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The Matrix

A sick movie.
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Singular Matrix

If determinant of coefficient is 0.
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Finding the inverse of a matrix

A⁻₁ = 1 ÷ Discriminant of A x |d -b| |-c a| This is useful because in the typical equation you can just multiply constants by inverse of coefficient and get your solution.
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Solving Linear Inequalities

1. Simplify each side by distributing or combining like terms 2. Move the variables to the same side of the equation/inequality 3. Isolate the term with the variable. 4. Isolate the variable. IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE NUMBER YOU MUST SWITCH THE INEQUALITY SIGN!! (sorry for yelling).
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Unions and Intersections.

The union of two sets is all the numbers in the two sets. It’s symbol is a \”U\” (The U of Miami). It’s word is \”or\”. The intersection of two sets is all the numbers that belong to both of the sets (which are in both, not all). It is symbolized by an upside down U. It’s word is \”and\”.
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Absolute Value inequalities

example: |y|>5 y>5 or y<-5
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Absolute values in Combined Inequalities

1. Break it down (if needed) 2. Do both + and – of 2 sides. 3. Do graphs for both. 4. Find intersects. 5. Graph and state answer.
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Absolute Value Inequalities Pattern

|x|>a then it’s an \”or\” statement. |x|<a then it's an \"and\" statement.
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Probability

favorable outcomes over total outcomes.
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Mutually Exclusive Events

2 events that have no outcomes in common.
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1. If two events A and B are mutually exclusive, then P(A) +P(B) 2. If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B)
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Independent Events

Two or more events in which the occurrence of one event does not affect the probability of the occurrence of the next event.
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Multiplication Rule for Probabilities