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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?\newline□\square meters

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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?\newline□\square meters
  1. Evaluate Function at x=0x=0: To find the height of the ball when it is thrown, we need to evaluate the function h(x)h(x) at the time xx when the ball is thrown, which is at x=0x = 0 seconds.
  2. Plug x=0x=0 into Equation: Plug x=0x = 0 into the equation h(x)=−(x−2)2+16.h(x) = -(x - 2)^2 + 16.\newlineh(0)=−(0−2)2+16h(0) = - (0 - 2)^2 + 16
  3. Calculate Value Inside Parentheses: Calculate the value inside the parentheses first: (0−2)2=(−2)2=4(0 - 2)^2 = (-2)^2 = 4.
  4. Substitute Value Back: Now, substitute the value back into the equation: h(0)=−4+16h(0) = -4 + 16.
  5. Perform Subtraction: Perform the subtraction: h(0)=12h(0) = 12.

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