Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They can be represented using symbols such as ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than). In this case, the inequality x^2 + (y + 3)^2 ≤ 16 indicates that the values of x and y must satisfy this condition, defining a region on the graph.
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Graphing Circles
The given inequality resembles the equation of a circle, which is typically expressed as (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Here, the expression x^2 + (y + 3)^2 = 16 represents a circle centered at (0, -3) with a radius of 4. The inequality indicates that we are interested in the area inside or on the boundary of this circle.
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Coordinate Plane
The coordinate plane is a two-dimensional surface formed by the intersection of a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is defined by an ordered pair (x, y). Understanding how to plot points and shapes on the coordinate plane is essential for visualizing inequalities and their corresponding regions, such as the area defined by the circle in this problem.
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Graphs & the Rectangular Coordinate System