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

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) = -2x^2 + 20x + 48. The x-coordinate of the vertex of a parabola given by the equation ax^2 + bx + c is found using the formula -b/(2a).Apply Formula: First, identify the coefficients a, b, and c in the quadratic equation h(x) = -2x^2 + 20x + 48. Here, a = -2, b = 20, and c = 48.Find X-coordinate: Next, apply the formula to find the x-coordinate of the vertex: x = -b/(2a). Plugging in the values of a and b, we get x = -20/(2 * -2).Calculate Time: Calculate the value of x: x = -20/(-4) = 5. This means that the hovercraft will reach its maximum height 5 seconds after takeoff.

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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. $\newline$ Its height (in meters), $x$ seconds after takeoff, is modeled by: $\newline$ $h(x)=-2x^{2}+20x+48$ $\newline$ How many seconds after takeoff will the hovercraft reach its maximum height? $\newline$ $\text{seconds}$

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Q. A hovercraft takes off from a platform.

\newline

Its height (in meters),

x

seconds after takeoff, is modeled by:

\newline

h(x)=-2x^{2}+20x+48

\newline

How many seconds after takeoff will the hovercraft reach its maximum height?

\newline

\text{seconds}

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 $h(x) = -2x^2 + 20x + 48$ . The $x$ -coordinate of the vertex of a parabola given by the equation $ax^2 + bx + c$ is found using the formula $-\frac{b}{2a}$ .
Apply Formula: First, identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $h(x) = -2x^2 + 20x + 48$ . Here, $a = -2$ , $b = 20$ , and $c = 48$ .
Find X-coordinate: Next, apply the formula to find the x-coordinate of the vertex: $x = -\frac{b}{2a}$ . Plugging in the values of $a$ and $b$ , we get $x = -\frac{20}{2 \times -2}$ .
Calculate Time: Calculate the value of $x$ : $x = \frac{-20}{-4} = 5$ . This means that the hovercraft will reach its maximum height $5$ seconds after takeoff.