QuestionA ball is thrown from 6 feet high. Its height is modeled by . Find the max height and distance from release.
Studdy Solution
STEP 1
Assumptions1. The height of the ball, , can be modeled by the equation . The variable represents the ball's horizontal distance, in feet, from where it was thrown3. We are looking for the maximum height of the ball and the distance from the point of release where this occurs
STEP 2
The maximum height of the ball 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 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 distance from the point of release where the maximum height occurs. So, the maximum height occurs3 feet from the point of release.
STEP 6
To find the maximum height of the ball, plug in the x-coordinate of the vertex into the equation .
STEP 7
Calculate the maximum height of the ball.
The maximum height of the ball is7.2 feet, which occurs3 feet from the point of release.
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