Math Problem Statement
Solution
The graph displayed on your screen represents a quadratic function, which typically has the form . 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 . Therefore, the function is increasing on the interval from 0 to positive infinity, which is represented as .
Would you like to know more details about how this was determined or have any other questions?
Here are some related questions to consider:
- How do you determine the vertex of a quadratic function from its graph?
- What happens to the interval of increase if the parabola opens upwards?
- Can you calculate the exact coordinates of the vertex using the vertex formula?
- What does the derivative of a quadratic function tell you about its increasing and decreasing intervals?
- How does the value of the coefficient in 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
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