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Antoine 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 Antoine threw it, is modeled by: h(x)=-2x^(2)+4x+16 What is the height of the ball at the time it is thrown? meters

Antoine 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), \newlinexx seconds after Antoine threw it, is modeled by:\newlineh(x)=−2x2+4x+16h(x)=-2x^{2}+4x+16\newlineWhat is the height of the ball at the time it is thrown?\newlinemeters\text{meters}

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Q. Antoine 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), \newlinexx seconds after Antoine threw it, is modeled by:\newlineh(x)=−2x2+4x+16h(x)=-2x^{2}+4x+16\newlineWhat is the height of the ball at the time it is thrown?\newlinemeters\text{meters}
  1. Evaluate height function at time x=0x = 0: To find the height of the ball at the time it is thrown, we need to evaluate the height function h(x)h(x) at the time x=0x = 0, which is the moment Antoine throws the ball.\newlineCalculation: h(0)=−2(0)2+4(0)+16h(0) = -2(0)^2 + 4(0) + 16
  2. Substitute x=0x = 0 into the equation: Substitute x=0x = 0 into the equation to get the initial height.\newlineCalculation: h(0)=−2(0)2+4(0)+16=0+0+16=16h(0) = -2(0)^2 + 4(0) + 16 = 0 + 0 + 16 = 16

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