Questions and Answers
What does the term 'degree' refer to in algebra?
What is the leading coefficient?
Number in front of the term with the highest exponent
What is a constant in algebra?
A number by itself (no variables)
A quadratic is a degree 1 polynomial.
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What does FOIL stand for?
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What does it mean to factor in algebra?
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Define GCF Factoring.
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What is Trinomial Factoring?
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What is a parabola?
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The y-intercept of a quadratic function is the _____ when x = 0.
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The axis of symmetry of a quadratic function is always written as x =.
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What is the turning point or vertex of a quadratic function?
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What are the zeros or roots of a function?
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A parabola that opens up has a leading coefficient that is negative.
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The standard form of a quadratic function refers to the format where a is the leading coefficient and c is the constant.
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What is meant by 'completing the square'?
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What is the purpose of the Zero Product Law?
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What does 'at most' signify in inequalities?
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What does 'slope-intercept form' define?
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Study Notes
Polynomial Terminology
- Degree: Highest exponent in a polynomial.
- Leading Coefficient: Coefficient of the term with the highest exponent.
- Constant: A standalone number without variables.
- Quadratic: A polynomial of degree 2.
Factoring Techniques
- FOIL or BOX Method: Technique for multiplying two binomials.
- To Factor: Rewriting an expression as a product of factors.
- GCF Factoring: Identify the greatest common factor and factor it out.
- DPS Factoring: Factoring the difference of squares results in opposite binomials.
- Trinomial Factoring: Factors are two binomials where the product of the last terms equals the last term of the trinomial, and their sum equals the middle term.
Characteristics of Quadratic Functions
- Parabola: Graphical representation of a quadratic function.
- Y-Intercept: Value of the function when x = 0 (c-value).
- Axis of Symmetry: Vertical line through the vertex, represented as x = (x-coordinate of the vertex).
- Turning Point (Vertex): Maximum or minimum point where the parabola changes direction.
- Zeros/Roots: Points where f(x) = 0, corresponding to x-intercepts.
Parabola Orientation
- Concave Up: Opens upwards; leading coefficient positive (a > 0); vertex is minimum.
- Concave Down: Opens downwards; leading coefficient negative (a < 0); vertex is maximum.
Forms of Quadratic Functions
- Standard Form: f(x) = ax^2 + bx + c.
- Vertex Form: f(x) = a(x - h)^2 + k, where (h, k) is the vertex.
- Completing the Square: Method for converting standard form to vertex form by adding and subtracting the square of half the b-value.
Transformations and Characteristics
- Vertical Stretch: Occurs when a > 1, making the graph narrower.
- Vertical Compression: Occurs when 0 < a < 1, making the graph wider.
Advanced Concepts
- Zero Product Law: If the product of multiple quantities equals zero, at least one of them must be zero.
- Rational Numbers: Includes all integers and fractions; terminates or repeats in decimal form.
- Irrational Numbers: Decimals that do not terminate or repeat.
- Simplest Radical Form: Roots with no perfect square factors inside the radical.
Important Theorems and Formulas
- Quadratic Formula: For finding roots of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / 2a.
- Pythagorean Theorem: Relation in right triangles: a² + b² = c².
- Area of Rectangle: A = L × W (Length times Width).
- Horizontal Asymptote: A horizontal line that the graph approaches.
Function Types and Regression
- Decreasing Exponential Function: Characterized by 0 < b < 1.
- Increasing Exponential Function: Defined where b > 1.
- Linear Functions: Result from repeatedly adding the same amount.
- Exponential Functions: Result from repeatedly multiplying by the same amount.
- Exponential Regression: Fitting data to an exponential function.
Systems of Equations
- System of Equations: Collection of two or more equations connected by "AND".
- Solutions: Point (x, y) that satisfies all equations in the system.
- Graphical Solution: Intersection point of two graphs.
- Substitution Method: Solve one equation for a variable, substitute into the other.
- Elimination Method: Manipulate equations to eliminate a variable when added.
Miscellaneous Concepts
- Consecutive Integers: Series of integers like x, x+1, etc.
- Consecutive Even and Odd Integers: Even integers (x, x+2...) or odd integers (x, x+2...).
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Basic Operations:
- Product: Multiplication
- Sum: Addition
- Quotient: Division
- Difference: Subtraction
Inequalities
- Solutions to a System of Inequalities: Points that satisfy all inequalities.
- Graphing Inequalities: Shaded regions represent solutions to inequalities; intersections indicate solutions.
Graphing Methods on TI-Nspire
- Finding Roots: Menu for polynomial roots: menu 3, 3, 1.
- Performing Exponential Regression: Use menu an specified options on the scatter plot page.
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Test your knowledge of essential Algebra vocabulary with these flashcards designed for the Algebra 1 Regents Exam. Each card features key terms and definitions to help you master polynomial concepts and other important mathematical terminology. Perfect for quick review and study!
