Math Problem Statement
Solution
From the graph provided in the question:
-
Symmetry of the graph:
- The parabola representing the height of the javelin is symmetric about its vertex. From the graph, the vertex occurs at seconds.
- Therefore, the height of the javelin is symmetric about the line seconds.
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When the javelin is 20 feet above the ground:
- Observing the graph, the javelin reaches a height of 20 feet for the first time as it rises, and then again as it falls.
- From the graph, these points occur approximately at second (first time) and seconds (second time).
Final Answers:
- The height of the javelin above the ground is symmetric about the line seconds.
- The javelin is 20 feet above the ground for the first time at second and again at seconds.
Would you like a detailed explanation or have any additional questions?
Related Questions:
- What is the maximum height reached by the javelin, and at what time does it occur?
- How long does the javelin stay in the air before hitting the ground?
- How would you determine the height of the javelin at a specific time (e.g., )?
- Can you derive the quadratic equation that models the javelin's motion using its vertex and a point?
- How does the initial velocity affect the shape of the graph?
Tip: To analyze a quadratic graph, always identify the vertex, axis of symmetry, and points of intersection with key heights or the ground.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Graphs of Parabolas
Symmetry
Real-World Applications of Quadratics
Formulas
Axis of symmetry: t = -b/(2a)
Height at a given time using h(t) = at² + bt + c
Theorems
Properties of parabolas
Symmetry about the vertex
Suitable Grade Level
Grades 9-11
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