Math Problem Statement

What is the range of the function on the graph?

Solution

Looking at the graph, we see a parabola opening upwards. The vertex of the parabola appears to be at the point (2, -3). Since the parabola opens upwards, the lowest value on the graph is -3, and the function continues to increase without bound.

Thus, the range of the function is all real numbers greater than or equal to -3.

The correct answer is:

  • All the real numbers greater than or equal to -3.

Would you like any further details on this? Here are some related questions to explore:

  1. How do you determine the vertex of a quadratic function from its graph?
  2. What is the domain of this quadratic function?
  3. How can we express this quadratic function algebraically based on the graph?
  4. What are the zeros (x-intercepts) of the function from the graph?
  5. How does the direction in which a parabola opens affect its range?

Tip: When identifying the range of a quadratic function, focus on the direction the parabola opens and the y-coordinate of the vertex.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graphing Parabolas

Formulas

Standard form of a quadratic function: y = ax^2 + bx + c

Theorems

Properties of parabolas
Vertex theorem

Suitable Grade Level

Grades 8-10