QuestionAn athlete releases a shot at . The height is modeled by . Find the max height and distance.
Studdy Solution
STEP 1
Assumptions1. The height of the shot, , is given by the equation . is the shot's horizontal distance, in feet, from its point of release3. We are asked to find the maximum height of the shot and the distance from the point of release where this occurs
STEP 2
The maximum height of the shot occurs at the vertex of the parabola represented by the equation . The x-coordinate of the vertex of a parabola given by the equation is given by .
STEP 3
Plug in the values for and from the equation into the formula for the x-coordinate of the vertex to find the distance from the point of release where the maximum height occurs.
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 by plugging this value into the equation for .
STEP 6
Calculate the maximum height of the shot.
The maximum height of the shot is18. feet, which occurs35 feet from the point of release.
Was this helpful?