QuestionA ball is thrown from 8 feet high. Its height, , models its path. Find the max height and distance.
Studdy Solution
STEP 1
Assumptions1. The height of the ball, , is modeled by the quadratic 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 the point of release where this occurs
STEP 2
The maximum height of the ball can be found by determining the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex of a parabola is given by .
STEP 3
Now, plug in the values for and from the equation to calculate .
STEP 4
Calculate the .
STEP 5
The maximum height of the ball is the y-coordinate of the vertex, which can be found by substituting into the equation .
STEP 6
Substitute into the equation to calculate the maximum height.
STEP 7
Calculate the maximum height.
The maximum height of the ball is11.7 feet, which occurs4.25 feet from the point of release.
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