Ricardo throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Ricardo threw it, is modeled by w(x)=-5(x-8)(x+4) What is the maximum height that the stone will reach? meters

Question

Ricardo throws a stone off a bridge into a river below. The stone's height (in meters above the water),  x seconds after Ricardo threw it, is modeled by  w(x)=-5(x-8)(x+4) What is the maximum height that the stone will reach? meters

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Determine Parabola Vertex: The maximum height of the stone corresponds to the vertex of the parabola described by the quadratic function w(x) = -5(x - 8)(x + 4). Since the coefficient of the quadratic term is negative (-5), the parabola opens downwards, and the vertex will give us the maximum height.Calculate Average of Roots: To find the vertex of the parabola, we need to determine the x-coordinate of the vertex, which is the average of the roots of the quadratic equation. The roots are given by the factors (x - 8) and (x + 4), which are x = 8 and x = -4, respectively.Find X-Coordinate of Vertex: Calculate the average of the roots to find the x-coordinate of the vertex: x-coordinate of vertex = (8 + (-4)) / 2 = 4 / 2 = 2.Find Maximum Height: Now that we have the x-coordinate of the vertex, we can find the maximum height by evaluating the function w(x) at x = 2. w(2) = -5(2 - 8)(2 + 4).Evaluate Function at X=2: Perform the calculations inside the parentheses first: w(2) = -5(-6)(6).Perform Final Calculation: Now multiply the numbers together to find the maximum height: w(2) = -5 * -6 * 6 = 30 * 6 = 180.

Ricardo throws a stone off a bridge into a river below. $\newline$ The stone's height (in meters above the water), $x$ seconds after Ricardo threw it, is modeled by $\newline$ $w(x)=-5(x-8)(x+4)$ $\newline$ What is the maximum height that the stone will reach? $\newline$ $meters$

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