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 What is the maximum height that the hovercraft will reach? meters

Identify Function Type: Identify the type of function and the general form of the equation. The function h(x) = -2x^2 + 20x + 48 is a quadratic function, which has a general form of ax^2 + bx + c. The graph of a quadratic function is a parabola. Since the coefficient of x^2 is negative (-2), the parabola opens downwards, which means the vertex of the parabola will give us the maximum height of the hovercraft.Find Vertex x-coordinate: Find the x-coordinate of the vertex of the parabola. The x-coordinate of the vertex of a parabola given by the equation ax^2 + bx + c is found using the formula -b/(2a). In our case, a = -2 and b = 20. x-coordinate of the vertex = -b/(2a) = -20/(2 * -2) = -20/(-4) = 5.Calculate Maximum Height: Calculate the maximum height using the x-coordinate of the vertex. Now that we have the x-coordinate of the vertex, we can find the maximum height by plugging it into the original equation h(x). h(5) = -2(5)^2 + 20(5) + 48 h(5) = -2(25) + 100 + 48 h(5) = -50 + 100 + 48 h(5) = 50 + 48 h(5) = 98.

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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
What is the maximum height that the hovercraft will reach?
meters

A hovercraft takes off from a platform. $\newline$ Its height (in meters), $\newline$ $x$ seconds after takeoff, is modeled by: $\newline$ $h(x)=-2x^{2}+20x+48$ $\newline$ What is the maximum height that the hovercraft will reach? $\newline$ $\text{meters}$

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Q. A hovercraft takes off from a platform.

\newline

Its height (in meters),

\newline

x

seconds after takeoff, is modeled by:

\newline

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

\newline

What is the maximum height that the hovercraft will reach?

\newline

\text{meters}

Identify Function Type: Identify the type of function and the general form of the equation. $\newline$ The function $h(x) = -2x^2 + 20x + 48$ is a quadratic function, which has a general form of $ax^2 + bx + c$ . The graph of a quadratic function is a parabola. Since the coefficient of $x^2$ is negative ( $-2$ ), the parabola opens downwards, which means the vertex of the parabola will give us the maximum height of the hovercraft.
Find Vertex x-coordinate: Find the x-coordinate of the vertex of the parabola. $\newline$ The x-coordinate of the vertex of a parabola given by the equation $ax^2 + bx + c$ is found using the formula $-b/(2a)$ . In our case, $a = -2$ and $b = 20$ . $\newline$ x-coordinate of the vertex = $-b/(2a) = -20/(2 \times -2) = -20/(-4) = 5$ .
Calculate Maximum Height: Calculate the maximum height using the $x$ -coordinate of the vertex. $\newline$ Now that we have the $x$ -coordinate of the vertex, we can find the maximum height by plugging it into the original equation $h(x)$ . $\newline$ $h(5) = -2(5)^2 + 20(5) + 48$ $\newline$ $h(5) = -2(25) + 100 + 48$ $\newline$ $h(5) = -50 + 100 + 48$ $\newline$ $h(5) = 50 + 48$ $\newline$ $h(5) = 98$ .