In math, a parabola is a curve on a graph that is created from point, moving so that its distance from a specific point is equidistant to a fixed line. On a standard x, y graph, a parabola looks like a “U” shaped line that can open up or down. A parabola has a domain and range that are dependent upon the vertex, or its central point, and the direction in which the “U” shape opens. The range is the set of all numbers that can hold a value for y. Generally, parabolas are generated from the function, f(x) = ax^2+ bx + c.
Analyze the parabola on the graph. Find the vertex, or the point on the graph where the parabola begins.
Find the y coordinate. Look at the vertex of the parabola and find where it hits on the y axis. Note the y coordinate. The y axis is the vertical line on the graph while the x axis is the horizontal line. For example, a vertex of (0, -3) means the central point of the parabola is on the y axis at the -3 coordinate.
Look at the direction that the parabola opens – up or down. If it opens up, then the range is [-3, ∞) to use the previous example. This means that all the values of y start with -3 and continue to infinity going up. If the parabola opens down, then the range is [-∞, -3) meaning the values of y continue infinitely down from -3.
For parabolas f(x) = ax^2+ bx + c, you can also find the range using the equation [f (-b/2a),∞) for a parabola that opens upward or (-∞, f (-b/2a)] if it open downward.