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

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Full solution

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), x x seconds after Antoine threw it, is modeled by:\newlineh(x)=−2x2+4x+16 h(x)=-2 x^{2}+4 x+16 \newlineWhat is the height of the ball at the time it is thrown?\newline□ \square meters
  1. Evaluate h(x)h(x) at x=0x=0: To find the height of the ball at the time it is thrown, we need to evaluate the function h(x)h(x) at x=0x = 0, because that's when Antoine just threw the ball.
  2. Plug x=0x=0 into h(x)h(x): Plug x=0x = 0 into the equation h(x)=−2x2+4x+16h(x) = -2x^{2} + 4x + 16.\newlineh(0)=−2(0)2+4(0)+16h(0) = -2(0)^{2} + 4(0) + 16
  3. Simplify the equation: Simplify the equation:\newlineh(0)=−2(0)+4(0)+16h(0) = -2(0) + 4(0) + 16\newlineh(0)=0+0+16h(0) = 0 + 0 + 16\newlineh(0)=16h(0) = 16

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