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Ying is a professional deep water free diver. His altitude (in meters relative to sea level), x seconds after diving, is modeled by: D(x)=(1)/(36)(x-60)^(2)-100 How many seconds after diving will Ying reach his lowest altitude? seconds

Ying is a professional deep water free diver.\newlineHis altitude (in meters relative to sea level), \newlinexx seconds after diving, is modeled by:\newlineD(x)=136(x−60)2−100D(x)=\frac{1}{36}(x-60)^{2}-100\newlineHow many seconds after diving will Ying reach his lowest altitude?\newlineseconds\text{seconds}

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Q. Ying is a professional deep water free diver.\newlineHis altitude (in meters relative to sea level), \newlinexx seconds after diving, is modeled by:\newlineD(x)=136(x−60)2−100D(x)=\frac{1}{36}(x-60)^{2}-100\newlineHow many seconds after diving will Ying reach his lowest altitude?\newlineseconds\text{seconds}
  1. Find Vertex of Parabola: To find the lowest altitude, we need to determine the vertex of the parabola represented by the function D(x)D(x) since the coefficient of the squared term is positive, indicating that the parabola opens upwards and the vertex will give the minimum value.
  2. Quadratic Equation Form: The function D(x)D(x) is in the form of a quadratic equation D(x)=a(x−h)2+kD(x) = a(x-h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. In this case, D(x)=136(x−60)2−100D(x) = \frac{1}{36}(x-60)^2 - 100, so the vertex is at (h,k)=(60,−100)(h, k) = (60, -100).
  3. Time of Lowest Altitude: The xx-coordinate of the vertex, hh, represents the time in seconds after diving when Ying will reach his lowest altitude. Since h=60h = 60, Ying will reach his lowest altitude 6060 seconds after diving.
  4. Direct Information from Vertex Form: We have found the time it takes for Ying to reach his lowest altitude without needing to perform any further calculations or solve any equations, as the vertex form of the quadratic function directly provides this information.

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