Quadrant

Definition

A quadrant is one of the four equal parts into which a plane or a sphere is divided by two intersecting lines or planes that are perpendicular to each other. It is a fundamental concept in the Cartesian coordinate system and is essential for understanding the graphing of linear and quadratic equations in two variables.

5 Must Know Facts For Your Next Test

1. The four quadrants in the Cartesian coordinate system are labeled I, II, III, and IV, and are defined by the positive and negative signs of the x and y coordinates.
2. Quadrant I is the region where both the x and y coordinates are positive, Quadrant II is where the x coordinate is negative and the y coordinate is positive, Quadrant III is where both the x and y coordinates are negative, and Quadrant IV is where the x coordinate is positive and the y coordinate is negative.
3. The sign of the slope of a linear equation determines which quadrant(s) the line will intersect.
4. The vertex of a parabolic function (quadratic equation) is the point where the graph changes direction, and its location in a specific quadrant is determined by the sign of the coefficient of the $x^2$ term.
5. Identifying the quadrant(s) in which a graph lies can provide valuable information about the behavior and characteristics of the underlying function.

Review Questions

• Explain how the quadrants in the Cartesian coordinate system are defined and how they relate to the signs of the x and y coordinates.
  • The Cartesian coordinate system is divided into four quadrants, labeled I, II, III, and IV. The quadrants are defined by the positive and negative signs of the x and y coordinates. Quadrant I has positive x and y coordinates, Quadrant II has negative x and positive y coordinates, Quadrant III has negative x and y coordinates, and Quadrant IV has positive x and negative y coordinates. Understanding the quadrants and their corresponding coordinate signs is crucial for interpreting the behavior of linear and quadratic equations when graphed in the coordinate plane.
• Describe how the sign of the slope of a linear equation affects the quadrant(s) in which the line intersects.
  • The sign of the slope of a linear equation determines which quadrant(s) the line will intersect. A positive slope will result in a line that passes through Quadrants I and III, while a negative slope will produce a line that passes through Quadrants II and IV. This relationship between the slope sign and the quadrant intersections is important for analyzing the characteristics and behavior of linear equations graphed in the coordinate plane.
• Explain how the location of the vertex of a quadratic equation (in terms of quadrants) is related to the sign of the coefficient of the $x^2$ term.
  • The location of the vertex of a parabolic function (quadratic equation) in the coordinate plane is determined by the sign of the coefficient of the $x^2$ term. If the coefficient is positive, the vertex will be at the lowest point of the parabola, and the graph will open upward, intersecting Quadrants I and II or Quadrants III and IV. If the coefficient is negative, the vertex will be at the highest point of the parabola, and the graph will open downward, intersecting Quadrants I and IV or Quadrants II and III. Understanding this relationship between the vertex location and the sign of the $x^2$ coefficient is crucial for interpreting the characteristics and behavior of quadratic equations when graphed in the coordinate plane.

Related terms

Cartesian Coordinate System: A two-dimensional coordinate system that uses two perpendicular axes, the x-axis and the y-axis, to locate points in a plane.

Origin: The point where the x-axis and y-axis intersect, represented by the coordinates (0, 0).

Axis Intercepts: The points where a line or curve intersects the x-axis or y-axis.