Math Problem Statement
f(x)=–5(x–8)2.
Solution
The given function is:
Analysis of the Function
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General Form: This is a quadratic function in vertex form: Here, , , and .
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Vertex: The vertex of the parabola is at .
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Direction of Opening: Since , the parabola opens downward because the coefficient of the squared term is negative.
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Steepness: The absolute value of (here, ) determines the steepness of the parabola. A larger value of indicates a steeper graph.
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Axis of Symmetry: The axis of symmetry is the vertical line passing through the vertex, given by:
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Maximum Value: Since the parabola opens downward, the vertex represents the maximum value of the function: Thus, the maximum value is at .
Key Points:
- Vertex:
- Axis of Symmetry:
- Direction: Downward
- Maximum Value:
- Domain and Range:
- Domain:
- Range:
Would you like a graph or further details about this function?
Related Questions:
- What is the y-intercept of the function ?
- How do we calculate specific values of for given -values?
- How does changing the value of affect the parabola’s shape?
- What is the effect of shifting and in the vertex form of a quadratic equation?
- Can this function be rewritten in standard form ? If yes, how?
Tip:
When analyzing quadratic functions, always identify the vertex and axis of symmetry first—they are key to understanding the function's behavior.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex Form of a Quadratic Equation
Parabolas
Domain and Range
Formulas
f(x) = a(x - h)^2 + k
Theorems
Vertex form of quadratic equations
Properties of parabolas
Suitable Grade Level
Grades 8-10
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