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Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height (in meters above the ground), xx seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16h(x) = -(x-2)^2 + 16. What is the height of the ball at the time it is thrown.

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Q. Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height (in meters above the ground), xx seconds after Amir threw it, is modeled by: h(x)=−(x−2)2+16h(x) = -(x-2)^2 + 16. What is the height of the ball at the time it is thrown.
  1. Identify initial height: Identify the initial height of the ball.\newlineThe height of the ball when it is thrown can be found by evaluating the height function at the time the ball is thrown, which is at x=0x = 0.
  2. Substitute x=0x = 0: Substitute x=0x = 0 into the height function.\newlineThe height function is given by h(x)=−(x−2)2+16h(x) = -(x-2)^2 + 16. To find the height at the time the ball is thrown, we substitute x=0x = 0 into the function: h(0)=−(0−2)2+16h(0) = -(0-2)^2 + 16.
  3. Calculate height at x = 00: Calculate the height at x = 00.\newlineh(0)=−(0−2)2+16h(0) = -(0-2)^2 + 16\newlineh(0)=−(−2)2+16h(0) = -(-2)^2 + 16\newlineh(0)=−4+16h(0) = -4 + 16\newlineh(0)=12h(0) = 12

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