Math Problem Statement
Solution
Let’s solve the problem step by step. The function modeling Jason's height is given as:
where is time in seconds, and is height in feet.
Part (a): Time to reach the maximum height
The given function is a quadratic equation of the form , where:
The time to reach the maximum height of a parabola is calculated using the formula:
Substituting and :
Thus, it takes 0.5 seconds for Jason to reach his maximum height.
Part (b): Maximum height reached
To find the maximum height, substitute into the function :
Simplify step-by-step:
- Combine terms:
Thus, the highest point Jason reached was 484 feet.
Final Answers:
(a) It took Jason 0.5 seconds to reach his maximum height.
(b) The maximum height Jason reached was 484 feet.
Would you like further details or explanations?
Follow-up Questions:
- How would the graph of look, and what does the vertex represent?
- What is the significance of the negative coefficient of in the equation?
- How would you calculate the total time Jason was in the air before hitting the water?
- What would happen to the maximum height if the initial constant (480) were increased?
- Could this quadratic function represent any motion other than Jason’s jump? Why or why not?
Tip:
The vertex form of a quadratic equation is useful for quickly identifying maximum or minimum values. Rewrite in vertex form to confirm your calculations!
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex of a Parabola
Formulas
t = -b / (2a)
h(t) = -16t^2 + 16t + 480
Theorems
Vertex Theorem of Quadratic Functions
Suitable Grade Level
Grades 9-12
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