Math Problem Statement

On which interval is the function increasing?

Solution

The graph displayed on your screen represents a quadratic function, which typically has the form y=ax2+bx+cy = ax^2 + bx + c. For this particular function, the graph is a downward-opening parabola.

A quadratic function is increasing on the interval to the right of its vertex when the parabola opens downwards. From the graph, the vertex appears to be at x=0x = 0. Therefore, the function is increasing on the interval from 0 to positive infinity, which is represented as (0,)(0, \infty).

Would you like to know more details about how this was determined or have any other questions?

Here are some related questions to consider:

  1. How do you determine the vertex of a quadratic function from its graph?
  2. What happens to the interval of increase if the parabola opens upwards?
  3. Can you calculate the exact coordinates of the vertex using the vertex formula?
  4. What does the derivative of a quadratic function tell you about its increasing and decreasing intervals?
  5. How does the value of the coefficient aa in y=ax2+bx+cy = ax^2 + bx + c affect the shape of the parabola?

Tip: When determining intervals of increase or decrease from a graph, always look for changes in the direction of the curve—increasing when it rises, and decreasing when it falls.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Intervals
Graph Analysis

Formulas

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Theorems

Increasing and Decreasing Functions
Vertex Theorem for Quadratics

Suitable Grade Level

Grades 9-12