QuestionA ball is thrown from 7 feet high. Its height is modeled by . Find the max height and distance.
Studdy Solution
STEP 1
Assumptions1. The height of the ball, , is given by the equation . is 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 where it was thrown when 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 in the form is given by .
STEP 3
Substitute and into the formula for the x-coordinate of the vertex to find the distance from where the ball was thrown when it reaches its maximum height.
STEP 4
Calculate the value of .
STEP 5
Substitute into the equation to find the maximum height of the ball.
STEP 6
Calculate the value of .
The maximum height of the ball is8. feet (rounded to the nearest tenth), which occurs3.5 feet from the point of release.
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