QuestionAn athlete releases a shot at , modeled by . Find the max height and distance.
Studdy Solution
STEP 1
Assumptions1. The height of the shot put can be modeled by the quadratic function
. The shot put is released at an angle of
3. represents the shot's horizontal distance, in feet, from its point of release4. represents the height of the shot put, in feet
STEP 2
The maximum height of the shot put is given by the vertex of the parabola represented by the quadratic function. The x-coordinate of the vertex of a parabola given by the equation is given by .
STEP 3
Substitute the values of and from the equation into the formula to find the x-coordinate of the vertex.
STEP 4
Calculate the x-coordinate of the vertex.
STEP 5
The x-coordinate of the vertex is the horizontal distance from the point of release at which the maximum height occurs. So, the maximum height occurs40 feet from the point of release.
STEP 6
To find the maximum height of the shot put, substitute the x-coordinate of the vertex into the equation .
STEP 7
Calculate the maximum height.
The maximum height of the shot put is21.3 feet and this occurs40 feet from the point of release.
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