Math Problem Statement

What is the range

Solution

The image shows a graph with a parabola opening upwards. The vertex of the parabola appears to be at the point (0, -2), and the parabola extends infinitely upward.

Determining the Range:

  • Range: The range of a function is the set of all possible yy-values that the function can take.
  • Since the vertex of the parabola is the lowest point, the yy-values start from y=2y = -2 and increase infinitely upwards.

Thus, the range of this parabola is: Range=[2,)\text{Range} = [-2, \infty)

This means that the function can take any yy-value starting from 2-2 and extending to positive infinity.

Would you like to explore further? Here are some related questions:

  1. How do you find the vertex of a parabola given its equation?
  2. What is the general form of a quadratic equation?
  3. How do the coefficients in a quadratic equation affect the shape of the parabola?
  4. What are the domain and range of a quadratic function?
  5. How do you determine the direction in which a parabola opens?

Tip: When determining the range of a quadratic function from its graph, look at the vertex and the direction the parabola opens. If it opens upwards, the range starts from the y-coordinate of the vertex and goes to infinity. If it opens downwards, the range goes from negative infinity up to the y-coordinate of the vertex.

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Math Problem Analysis

Mathematical Concepts

Graphing
Quadratic Functions
Range

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12