Math Problem Statement
solve for max point
Solution
The text in the image reads:
"The approximate height of a rock in meters, thrown upwards off a cliff, is where is time in seconds. What is the maximum height of the rock?"
This problem requires finding the maximum height of the rock, which involves determining the vertex of the quadratic function .
Steps to Solve:
The height function is a quadratic function of the form , where:
For a quadratic function , the time at which the maximum height occurs can be found using the formula:
Substitute the values of and :
Now, substitute second back into the height function to find the maximum height:
Answer:
The maximum height of the rock is 185 meters.
Would you like more details or have any further questions?
Related Questions:
- What is the significance of the coefficient being negative in the quadratic function?
- How can you determine the time when the rock hits the ground?
- What would happen to the maximum height if the initial velocity of the rock was doubled?
- How does the maximum height change if the rock is thrown from a lower cliff?
- Can you derive the general formula for the vertex of any quadratic function?
Tip:
When dealing with quadratic functions, remember that the vertex represents the maximum or minimum point. The sign of the coefficient determines whether the parabola opens upwards (minimum) or downwards (maximum).
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Vertex of a Parabola
Formulas
Quadratic function formula h(t) = at^2 + bt + c
Vertex formula t_max = -b/(2a)
Theorems
-
Suitable Grade Level
High School