Questions and Answers
What does Quadrant I represent?
What does Quadrant II represent?
What does Quadrant III represent?
What does Quadrant IV represent?
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What is the x-intercept?
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What is the y-intercept?
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What is the distance formula?
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What is the midpoint formula?
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What is the slope-intercept form?
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What is the point-slope form?
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What is the standard form of a line?
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What does parallel slope mean?
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What are parallel lines?
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What does perpendicular slope mean?
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What are perpendicular lines?
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What is the quadratic formula?
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What is the square root property?
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What is a linear equation?
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What is a rational equation?
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What is a radical equation?
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What is a quadratic equation?
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What is the quadratic form?
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What is an absolute value equation?
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What is a linear inequality?
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What is an absolute value inequality?
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What is a compound inequality?
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What are extraneous solutions?
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What is an identity equation?
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What is a conditional equation?
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What is an inconsistent equation?
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What is the origin?
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What is a polynomial equation?
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What is slope?
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What is zero slope?
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What is undefined slope?
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What does y = b represent?
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What does x = a represent?
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Study Notes
Coordinate Plane Quadrants
- Quadrant I: Both x and y coordinates are positive (+,+).
- Quadrant II: x-coordinate is negative and y-coordinate is positive (-,+).
- Quadrant III: Both x and y coordinates are negative (-,-).
- Quadrant IV: x-coordinate is positive and y-coordinate is negative (+,-).
Intercepts
- x-intercept: The x-coordinate where a graph crosses the x-axis; y-coordinate at this point is zero.
- y-intercept: The y-coordinate where a graph crosses the y-axis; x-coordinate at this point is zero.
Essential Formulas
- Distance Formula: Calculate distance between two points (x₁, y₁) and (x₂, y₂) using d = √[(x₂ - x₁)² + (y₂ - y₁)²].
- Midpoint Formula: Find the midpoint between two points by using ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-Slope Form: (y - y₁) = m(x - x₁), with m as the slope and (x₁, y₁) as a point on the line.
- Standard Form of a Line: Ax + By = C, with A and B as integers.
Line Properties
- Parallel Lines: Maintain the same slope and do not intersect.
- Perpendicular Lines: Intersect at right angles; slopes are negative reciprocals of each other.
Quadratics
- Quadratic Formula: x = [-b ± √(b² - 4ac)]/(2a) for solving quadratic equations.
- Square Root Property: For any real number n, if x² = n, then x = ±√n.
- Quadratic Equation: An equation of the form ax² + bx + c = 0, where a ≠ 0.
- Quadratic Form: Represented as au² + bu + c, where u is any expression in x.
Types of Equations
- Linear Equation: A straight line equation, typically in the form ax + b = 0.
- Rational Equation: Contains one or more rational expressions (fractions).
- Radical Equation: Involves variables under a radical symbol.
- Absolute Value Equation: Contains an absolute value expression.
- Linear Inequality: Formed by replacing the equal sign in a linear equation with an inequality symbol.
- Absolute Value Inequality: An inequality that includes an absolute value expression.
Solutions and Equations
- Extraneous Solutions: Solutions that are invalid in the context of the original equation.
- Identity Equation: True for all values of the variable.
- Conditional Equation: True for some values of the variable.
- Inconsistent Equation: An equation that leads to a false statement.
Coordinate System Basics
- Origin: The point (0,0), where the x-axis and y-axis intersect.
Polynomial Characteristics
- Polynomial Equation: Contains only polynomial terms.
Slope Concepts
- Slope: Defined as the change in y-values over the change in x-values.
- Zero Slope: Indicates a horizontal line.
- Undefined Slope: Indicates a vertical line.
- Horizontal Line Equation: Represented as y = b.
- Vertical Line Equation: Represented as x = a.
Studying That Suits You
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Description
Test your knowledge of the coordinate plane with these flashcards from OpenStax College Algebra Chapter 2. Learn about the characteristics of each quadrant and reinforce your understanding of x and y coordinates. Perfect for students looking to enhance their algebra skills.