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Rajani kicks a football. Its height in feet is given by h=-16t^(2)+24 t where t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point? Answer: seconds

Rajani kicks a football. Its height in feet is given by h=−16t2+24t h=-16 t^{2}+24 t where t t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point?\newlineAnswer: seconds

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Q. Rajani kicks a football. Its height in feet is given by h=−16t2+24t h=-16 t^{2}+24 t where t t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point?\newlineAnswer: seconds
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation h=−16t2+24th=-16t^2+24t. The equation is in the form at2+bt+cat^2 + bt + c, where a=−16a = -16, b=24b = 24, and bb00 (since it is not written, it is implied that bb11).
  2. Find vertex time: Find the tt-coordinate of the vertex of the parabola, which represents the time at which the football reaches its maximum height.\newlineThe formula for the tt-coordinate of the vertex in a quadratic equation at2+bt+cat^2 + bt + c is t=−b2at = -\frac{b}{2a}.\newlineSubstitute a=−16a = -16 and b=24b = 24 into the formula: t=−242∗(−16)t = -\frac{24}{2*(-16)}.
  3. Calculate time: Calculate the time at which the football reaches its maximum height. t=−242⋅(−16)=−24−32=2432=0.75t = -\frac{24}{2 \cdot (-16)} = \frac{-24}{-32} = \frac{24}{32} = 0.75
  4. Round to nearest second: Round the answer to the nearest second.\newlineThe time at which the football reaches its maximum height is 0.750.75 seconds, which rounds to 11 second when considering the nearest whole second.

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