OpenStax College Algebra Ch 2 Flashcards
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Questions and Answers

What does Quadrant I represent?

  • (+, +) (correct)
  • (-, +)
  • (-, -)
  • (+, -)

    • What does Quadrant II represent?

  • (-, -)
  • (+, +)
  • (-, +) (correct)
  • (+, -)

    • What does Quadrant III represent?

  • (-, +)
  • (+, -)
  • (+, +)
  • (-, -) (correct)

    • What does Quadrant IV represent?

    <p>(+, -)</p> Signup and view all the answers

    What is the x-intercept?

    <p>x coordinate of a point where a graph crosses the x-axis</p> Signup and view all the answers

    What is the y-intercept?

    <p>y coordinate of a point where a graph crosses the y-axis</p> Signup and view all the answers

    What is the distance formula?

    <p>d = √[(x₂ - x₁)² + (y₂ - y₁)²]</p> Signup and view all the answers

    What is the midpoint formula?

    <p>(x₁+x₂)/2, (y₁+y₂)/2</p> Signup and view all the answers

    What is the slope-intercept form?

    <p>y = mx + b</p> Signup and view all the answers

    What is the point-slope form?

    <p>(y - y₁) = m(x - x₁)</p> Signup and view all the answers

    What is the standard form of a line?

    <p>Ax + By = C</p> Signup and view all the answers

    What does parallel slope mean?

    <p>Slopes are the same</p> Signup and view all the answers

    What are parallel lines?

    <p>Lines that always have the same slope and do not intersect</p> Signup and view all the answers

    What does perpendicular slope mean?

    <p>negative reciprocal</p> Signup and view all the answers

    What are perpendicular lines?

    <p>Two intersecting lines that form right angles</p> Signup and view all the answers

    What is the quadratic formula?

    <p>x = [-b ± √(b² - 4ac)]/(2a)</p> Signup and view all the answers

    What is the square root property?

    <p>If x² = n, then x = ±√n</p> Signup and view all the answers

    What is a linear equation?

    <p>An equation of a straight line, written in one variable.</p> Signup and view all the answers

    What is a rational equation?

    <p>An equation that contains one or more rational expressions</p> Signup and view all the answers

    What is a radical equation?

    <p>Equations that contain variables under a radical symbol</p> Signup and view all the answers

    What is a quadratic equation?

    <p>An equation containing a second-degree polynomial</p> Signup and view all the answers

    What is the quadratic form?

    <p>The form au² + bu + c</p> Signup and view all the answers

    What is an absolute value equation?

    <p>An equation containing an absolute value expression</p> Signup and view all the answers

    What is a linear inequality?

    <p>An inequality formed by replacing the equal sign in a linear equation with an inequality symbol</p> Signup and view all the answers

    What is an absolute value inequality?

    <p>An inequality that contains an absolute value expression</p> Signup and view all the answers

    What is a compound inequality?

    <p>Two inequalities combined into one statement</p> Signup and view all the answers

    What are extraneous solutions?

    <p>An apparent solution that must be rejected</p> Signup and view all the answers

    What is an identity equation?

    <p>An equation that is true for all values of the variable</p> Signup and view all the answers

    What is a conditional equation?

    <p>An equation that is true for some values of the variable</p> Signup and view all the answers

    What is an inconsistent equation?

    <p>An equation producing a false result</p> Signup and view all the answers

    What is the origin?

    <p>The point (0,0) where the x-axis and the y-axis intersect</p> Signup and view all the answers

    What is a polynomial equation?

    <p>An equation that contains only polynomial terms</p> Signup and view all the answers

    What is slope?

    <p>The change in y-values over the change in x-values</p> Signup and view all the answers

    What is zero slope?

    <p>The slope of a horizontal line</p> Signup and view all the answers

    What is undefined slope?

    <p>The slope of a vertical line</p> Signup and view all the answers

    What does y = b represent?

    <p>Equation of a horizontal line</p> Signup and view all the answers

    What does x = a represent?

    <p>Equation of a vertical line</p> Signup and view all the answers

    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.

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    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.

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