Ming throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Ming threw it, is modeled by: h(x)=-5(x-1)^(2)+45 What is the maximum height that the stone will reach? meters

Identify Function Type: Identify the type of function and its properties. The function h(x) = -5(x-1)² + 45 is a quadratic function in the form of h(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola. Since the coefficient of the squared term is negative (a = -5), the parabola opens downwards, which means the vertex is the maximum point of the function.Determine Vertex: Determine the vertex of the parabola. The vertex form of the quadratic function gives us the vertex directly. The vertex (h, k) of the function h(x) = -5(x-1)² + 45 is (1, 45). This means the maximum height of the stone is 45 meters, which occurs at x = 1 second.

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Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water),
x seconds after Ming threw it, is modeled by:

h(x)=-5(x-1)^(2)+45
What is the maximum height that the stone will reach?
meters

Ming throws a stone off a bridge into a river below. $\newline$ The stone's height (in meters above the water), $\newline$ $x$ seconds after Ming threw it, is modeled by: $\newline$ $h(x)=-5(x-1)^{2}+45$ $\newline$ What is the maximum height that the stone will reach? $\newline$ $\text{meters}$

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Q. Ming throws a stone off a bridge into a river below.

\newline

The stone's height (in meters above the water),

\newline

x

seconds after Ming threw it, is modeled by:

\newline

h(x)=-5(x-1)^{2}+45

\newline

What is the maximum height that the stone will reach?

\newline

\text{meters}

Identify Function Type: Identify the type of function and its properties. $\newline$ The function $h(x) = -5(x-1)^2 + 45$ is a quadratic function in the form of $h(x) = a(x-h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. Since the coefficient of the squared term is negative $(a = -5)$ , the parabola opens downwards, which means the vertex is the maximum point of the function.
Determine Vertex: Determine the vertex of the parabola. $\newline$ The vertex form of the quadratic function gives us the vertex directly. The vertex $(h, k)$ of the function $h(x) = -5(x-1)^2 + 45$ is $(1, 45)$ . This means the maximum height of the stone is $45$ meters, which occurs at $x = 1$ second.