Questions and Answers
What is a binomial?
Roots of a parabola aka _____
zeros
What is the standard form of a quadratic equation?
y = ax² + bx + c
What is the discriminant of a quadratic equation?
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If the discriminant is negative, the quadratic function has imaginary zeros.
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What is the vertex form of a quadratic equation?
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The minimum/maximum of a parabola is what?
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When a > 0, the parabola opens _____ and gives the _____
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What is the definition of a permutation?
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What is the definition of a combination?
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What is the definition of a logarithm?
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What do you need to do when manipulating logarithms?
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What are matrices?
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What does completing the square involve?
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In how many ways can 4 boys be seated in 4 chairs if two boys always sit adjacent to each other?
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From a group of 9 different books, how many arrangements are possible if 4 books are to be selected and arranged on a shelf?
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What is the permutation formula?
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What is the combination formula?
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What is the result of 2√7 x 2√7?
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Study Notes
Algebra 2 Key Concepts
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Binomial: An expression with two distinct terms, such as x + y.
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Roots of a Parabola: Also known as zeros, these are the x-values where the quadratic function intersects the x-axis.
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Quadratic Equation: Represented as y = ax² + bx + c, where a, b, and c are constants.
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Discriminant: Calculated as b² - 4ac, it indicates the number of roots a quadratic function has.
- If negative, the function has no real roots (imaginary roots).
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Vertex Form of Quadratic: Expressed as y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
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Vertex Minimum/Maximum: The y-value of the vertex represents the minimum (if a > 0) or maximum (if a < 0) of the parabola.
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Parabola Orientation: When a > 0, the parabola opens upwards, resulting in a minimum point; when a < 0, it opens downwards, yielding a maximum point.
Permutations and Combinations
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Permutation: Refers to arrangements of objects where order matters, calculable by the factorial of the number of objects involved.
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Combination: Arrangements of objects where order doesn’t matter, calculated using combinations formula.
Logarithms
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Logarithm: The inverse operation of exponentiation.
- Example: log₂64 = x translates to 2ˣ = 64, solving for x gives x = 6.
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Log Rules: Includes various properties for manipulating logarithmic expressions.
Matrices and Complements
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Matrices: Foundational for organizing data in rows and columns, requiring practice for understanding complex operations.
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Completing the Square: A method used to transform a quadratic equation into vertex form; involves practice for mastery.
Problem-Solving Examples
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Seating Arrangement with Adjacency Constraint: To calculate seating arrangements for 4 boys where 2 must sit next to each other, treat the 2 as a single unit. Results in 12 combinations by accounting for internal arrangements.
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Arranging Books: Selecting and arranging 4 books from 9 different titles can yield 3024 different arrangements using factorial calculations.
Formulas
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Permutation Formula: P(n, r) = n! / (n - r)! describes ways to arrange r objects from n total.
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Combination Formula: C(n, r) = n! / [r!(n - r)!] calculates ways to choose r objects from n without regard to order.
Multiplication of Radicals
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Example Calculation: For 2√7 x 2√7,
- Step 1: Collect like terms: 2 x 2 x √7 x √7
- Step 2: Simplify to 4 x √49 = 4 x 7 = 28.
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Description
Prepare for the SAT Math section with these essential flashcards focused on Algebra 2 concepts. Each card provides key definitions, including binomials and quadratic equations, to help reinforce your understanding. Perfect for quick review or in-depth study related to SAT Math topics.
