Questions and Answers
What is the slope-intercept form of a line?
What is Standard Form?
Ax+By=C
What is Point-Slope Form?
y - y1 = m(x - x1)
What are real numbers?
Signup and view all the answers
The order of operations is defined as Parentheses, Exponents, Addition, Subtraction, Multiplication, and Division.
Signup and view all the answers
What does a 'No Solution' in a linear equation indicate?
Signup and view all the answers
What does 'All Real Numbers' mean in solving a linear equation?
Signup and view all the answers
Define a relation.
Signup and view all the answers
What is the domain in a function?
Signup and view all the answers
What is the range in a function?
Signup and view all the answers
A function is a relation where no input has exactly one output.
Signup and view all the answers
What indicates if a relation is a function using the Vertical Line Test?
Signup and view all the answers
What does f(x) mean?
Signup and view all the answers
What is the formula for slope?
Signup and view all the answers
What does m represent in slope?
Signup and view all the answers
What does the variable b represent in the slope-intercept form?
Signup and view all the answers
How do you find an equation of a line that passes through two points?
Signup and view all the answers
What does the Discriminant tell you?
Signup and view all the answers
If b² - 4ac > 0, the equation has two imaginary solutions.
Signup and view all the answers
If b² - 4ac = 0, the equation has two real solutions.
Signup and view all the answers
If b² - 4ac < 0, the equation has two real solutions.
Signup and view all the answers
What is the Quadratic Formula?
Signup and view all the answers
Study Notes
Algebra Concepts and Definitions
- Slope-intercept Form: Expressed as y = mx + b, where m is the slope and b is the y-intercept.
- Standard Form: Written as Ax + By = C, encompassing all linear equations.
- Point-Slope Form: Given as y - y1 = m(x - x1) for a line passing through point (x1, y1) with slope m.
- Real Numbers: Consist of both rational and irrational numbers, encompassing all possible values along the number line.
- Order of Operations (PEMDAS): A mnemonic for solving expressions in the order of Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Linear Equations
- No Solution: Occurs when contradictory equations, e.g., 10 = -3, arise when solving.
- All Real Numbers: Happens when the equation simplifies to a true statement, such as 0 = 0.
- Relation: A pairing of input and output values, typically represented as coordinate points (x, y).
- Domain: The set of all possible input values (x values) for a relation.
- Range: The collection of all output values (y values) corresponding to the domain.
Functions
- Function: A relation where each input has exactly one output; x values cannot repeat.
- Vertical Line Test: A graphical method to determine if a relation is a function; a vertical line should intersect the graph at most once.
- Function Notation: Represented as f(x), indicating the value of the function for a given x.
Slope and Line Characteristics
- Slope (m): Defined as rise/run, or (y2 - y1) / (x2 - x1).
- Positive Slope: Indicates an upward line.
- Negative Slope: Represents a downward line.
- Zero Slope: Characterizes a horizontal line.
- Undefined Slope: Pertains to a vertical line, denoted as m = number/0.
- Parallel Lines: Lines with identical slopes that never intersect.
- Perpendicular Lines: Lines intersecting at right angles; their slopes are opposite reciprocals, e.g., m1 * m2 = -1.
Quadratic Functions and Equations
- Quadratic Formula: x = -b ± √(b² - 4ac) / 2a, used to find roots of quadratic equations.
-
Discriminant (b² - 4ac): Indicates the nature of the roots of a quadratic equation;
- Greater than zero indicates two real solutions.
- Equal to zero indicates one real solution.
- Less than zero indicates two imaginary solutions.
- Completing the Square: A method for solving quadratic equations, rearranging them into a perfect square trinomial.
Graphing Quadratics
- Vertex: The highest or lowest point of a parabola formed by a quadratic function.
- Axis of Symmetry: The vertical line that divides the parabola into two symmetrical halves, passing through the vertex.
-
Graphing Quadratic Inequalities:
- Parabola drawn based on the inequality type; dashed for > or <, solid for ≥ or ≤.
- Test points inside the parabola to determine shaded regions.
Polynomial Theorems
- Rational Zero Theorem: Provides potential rational roots based on the factors of the constant term and leading coefficient.
- Factor Theorem: States that (x - k) is a factor of polynomial f(x) if f(k) = 0.
- Remainder Theorem: The remainder of f(x) divided by (x - k) is f(k).
- Fundamental Theorem of Algebra: Asserts that any polynomial of degree n has at least one complex root.
Complex Numbers
- Complex Conjugates: Two complex numbers of form a + bi and a - bi; their product yields a real number.
- Absolute Value of Complex Numbers: Calculated as |z| = √(a² + b²), where a and b are real and imaginary components respectively.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key Algebra 2 concepts with these flashcards. Each card provides a definition of important terms, including different forms of equations and the order of operations. Perfect for students looking to reinforce their understanding of algebraic principles.
