QuestionAn athlete releases a shot modeled by . Find the maximum height and its distance from release.
Studdy Solution
STEP 1
Assumptions1. The height of the shot put is modeled by the function . represents the horizontal distance from the point of release in feet3. We are looking for the maximum height of the shot put and the distance from the point of release at which this occurs
STEP 2
The maximum height of the shot put occurs at the vertex of the parabola represented by the function . Since the function is in the form , the x-coordinate of the vertex can be found using the formula .
STEP 3
Plug in the values for and from the function into the formula to find the x-coordinate of the vertex.
STEP 4
Calculate the x-coordinate of the vertex.
STEP 5
Now that we have the x-coordinate of the vertex, we can find the maximum height of the shot put by plugging this value into the function .
STEP 6
Calculate the maximum height of the shot put.
The maximum height of the shot put is18.4 feet, which occurs35 feet from the point of release.
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