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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), x seconds after Amir threw it, is modeled by: h(x)=-(x-2)^(2)+16 What is the height of the ball at the time it is thrown? meters

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

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Full solution

Q. Amir stands on a balcony and throws a ball to his dog, who is at ground level.\newlineThe ball's height (in meters above the ground), xx seconds after Amir threw it, is modeled by:\newlineh(x)=−(x−2)2+16h(x) = -(x - 2)^{2} + 16\newlineWhat is the height of the ball at the time it is thrown?\newlinemetersmeters
  1. Identify initial time: Identify the initial time of the throw. The initial time of the throw is when x=0x = 0 seconds, since xx represents the time in seconds after Amir threw the ball.
  2. Substitute into equation: Substitute the initial time into the height equation.\newlineTo find the height of the ball at the time it is thrown, we substitute x=0x = 0 into the height equation h(x)=−(x−2)2+16h(x) = -(x - 2)^2 + 16.\newlineh(0)=−(0−2)2+16h(0) = - (0 - 2)^2 + 16
  3. Calculate initial height: Calculate the height at the initial time.\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 meters

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