Math Problem Statement
Solution
The image shows a parabola, and the question asks to "Determine the domain on which the following function is increasing."
For a quadratic function in the form of a parabola (like the one in the image), the domain where the function is increasing refers to the interval of x-values where the slope of the curve is positive (the curve is going upward).
Key Points:
- The parabola opens downward, which means it has a maximum point at its vertex.
- The function increases to the left of the vertex.
To solve:
- Find the vertex of the parabola: This will give us the turning point where the function changes from increasing to decreasing.
- Determine the domain where the function is increasing: This will be for x-values less than the x-coordinate of the vertex.
If you provide the specific coordinates or more details about the graph, I can pinpoint the exact domain.
Would you like to provide further details or ask more questions related to this?
Related Questions:
- How do you find the vertex of a quadratic function algebraically?
- Can you explain the difference between the domain and the range of a function?
- What are the characteristics of a function that is increasing or decreasing?
- How does the concavity of a parabola affect where it's increasing or decreasing?
- How can the first derivative help in determining where a function increases or decreases?
Tip:
For a parabola, the x-coordinate of the vertex can be found using the formula , where the quadratic equation is in the form .
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Parabolas
Formulas
Vertex formula x = -b / 2a
Quadratic equation: ax^2 + bx + c = 0
Theorems
Properties of parabolas
Increasing/Decreasing Intervals for Quadratic Functions
Suitable Grade Level
Grades 9-11
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