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 its properties. The function h(x) = -2x^2 + 20x + 48 is a quadratic function, which graphs as a parabola. Since the coefficient of x^2 is negative (-2), the parabola opens downwards, which means it has a maximum point at its vertex.Find Vertex x-coordinate: Find the x-coordinate of the vertex. The x-coordinate of the vertex of a parabola given by the function f(x) = ax^2 + bx + c is found using the formula x = -b/(2a). For our function h(x) = -2x^2 + 20x + 48, a = -2 and b = 20. x = -b/(2a) = -20/(2 * -2) = -20/(-4) = 5Find Vertex y-coordinate: Find the y-coordinate of the vertex, which is the maximum height. Substitute x = 5 into the function h(x) to find the maximum height. 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), $x$ seconds after takeoff, is modeled by: $\newline$ $h(x)=-2 x^{2}+20 x+48$ $\newline$ What is the maximum height that the hovercraft will reach? $\newline$ $\square$ meters

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

\newline

What is the maximum height that the hovercraft will reach?

\newline

\square

meters

Identify Function Type: Identify the type of function and its properties. $\newline$ The function $h(x) = -2x^2 + 20x + 48$ is a quadratic function, which graphs as a parabola. Since the coefficient of $x^2$ is negative ( $-2$ ), the parabola opens downwards, which means it has a maximum point at its vertex.
Find Vertex x-coordinate: Find the x-coordinate of the vertex. $\newline$ The x-coordinate of the vertex of a parabola given by the function $f(x) = ax^2 + bx + c$ is found using the formula $x = -\frac{b}{2a}$ . For our function $h(x) = -2x^2 + 20x + 48$ , $a = -2$ and $b = 20$ . $\newline$ $x = -\frac{b}{2a} = -\frac{20}{2 \times -2} = -\frac{20}{-4} = 5$
Find Vertex y-coordinate: Find the y-coordinate of the vertex, which is the maximum height. $\newline$ Substitute $x = 5$ into the function $h(x)$ to find the maximum height. $\newline$ $h(5) = -2(5)^2 + 20(5) + 48$ $\newline$ $h(5) = -2(25) + 100 + 48$ $\newline$ $h(5) = -50 + 100 + 48$ $\newline$ $h(5) = 50 + 48$ $\newline$ $h(5) = 98$