Math Problem Statement
Solution
The graph in the image shows a downward-opening parabola, indicating a quadratic function. The function is decreasing where the graph slopes downward, to the right of the vertex.
Steps to determine the interval of decrease:
- The vertex is located at (where the graph reaches its maximum).
- The function decreases for values of greater than the vertex, i.e., for .
- The decreasing interval starts from and extends to positive infinity.
Answer:
The function is decreasing on the interval .
Let me know if you want more details or have any questions.
Here are some related questions to consider:
- How can we find the interval of increase for this function?
- What is the equation of this parabola based on the graph?
- What is the significance of the vertex in determining where the function decreases?
- How would the interval of decrease change if the parabola opened upwards?
- How do we generally find intervals of increase or decrease using calculus?
Tip: The derivative of a function can help identify where it is increasing or decreasing by analyzing the sign of the derivative.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Intervals of Increase and Decrease
Formulas
Standard form of a quadratic function: f(x) = ax^2 + bx + c
Theorems
The graph of a quadratic function is a parabola, and it decreases on the interval to the right of its vertex when a < 0.
Suitable Grade Level
Grades 9-10
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