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A hovercraft takes off from a platform. Its height (in meters), x seconds after takeoff, is modeled by: h(x)=-2x^(2)+20 x+48 How many seconds after takeoff will the hovercraft reach its maximum height? seconds

A hovercraft takes off from a platform.\newlineIts height (in meters), xx seconds after takeoff, is modeled by:\newlineh(x)=−2x2+20x+48h(x)=-2x^{2}+20x+48\newlineHow many seconds after takeoff will the hovercraft reach its maximum height?\newlineseconds\text{seconds}

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Q. A hovercraft takes off from a platform.\newlineIts height (in meters), xx seconds after takeoff, is modeled by:\newlineh(x)=−2x2+20x+48h(x)=-2x^{2}+20x+48\newlineHow many seconds after takeoff will the hovercraft reach its maximum height?\newlineseconds\text{seconds}
  1. Identify Coefficients: To find the time at which the hovercraft reaches its maximum height, we need to find the vertex of the parabola described by the quadratic equation h(x)=−2x2+20x+48h(x) = -2x^2 + 20x + 48. The xx-coordinate of the vertex of a parabola given by the equation ax2+bx+cax^2 + bx + c is found using the formula −b2a-\frac{b}{2a}.
  2. Apply Formula: First, identify the coefficients aa, bb, and cc in the quadratic equation h(x)=−2x2+20x+48h(x) = -2x^2 + 20x + 48. Here, a=−2a = -2, b=20b = 20, and c=48c = 48.
  3. Find X-coordinate: Next, apply the formula to find the x-coordinate of the vertex: x=−b2ax = -\frac{b}{2a}. Plugging in the values of aa and bb, we get x=−202×−2x = -\frac{20}{2 \times -2}.
  4. Calculate Time: Calculate the value of xx: x=−20−4=5x = \frac{-20}{-4} = 5. This means that the hovercraft will reach its maximum height 55 seconds after takeoff.

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