Algebra 1 Regents Exam Review Flashcards

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Questions and Answers

What does the term 'degree' refer to in algebra?

The number of terms in a polynomial

The sum of the coefficients

The type of polynomial

The polynomial's highest exponent (correct)

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.

False Signup and view all the answers

What does FOIL stand for?

First, Outside, Inside, Last Signup and view all the answers

What does it mean to factor in algebra?

To write an algebraic expression as an equivalent product Signup and view all the answers

Define GCF Factoring.

Find the greatest common factor among all the terms and then divide it out Signup and view all the answers

What is Trinomial Factoring?

The factors are 2 binomials where the numbers multiply to the last and add to the middle Signup and view all the answers

What is a parabola?

The graph of a quadratic function Signup and view all the answers

The y-intercept of a quadratic function is the _____ when x = 0.

c-value Signup and view all the answers

The axis of symmetry of a quadratic function is always written as x =.

True Signup and view all the answers

What is the turning point or vertex of a quadratic function?

The minimum or maximum point on a parabola Signup and view all the answers

What are the zeros or roots of a function?

When f(x) = 0 or y = 0 Signup and view all the answers

A parabola that opens up has a leading coefficient that is negative.

False Signup and view all the answers

The standard form of a quadratic function refers to the format where a is the leading coefficient and c is the constant.

True Signup and view all the answers

What is meant by 'completing the square'?

Find half the b-value, square it, add and subtract it Signup and view all the answers

What is the purpose of the Zero Product Law?

If 2 or more quantities have a product of zero, then at least one of them must be equal to zero. Signup and view all the answers

What does 'at most' signify in inequalities?

≤ Signup and view all the answers

What does 'slope-intercept form' define?

y = mx + b Signup and view all the answers

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...).
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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Description

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!