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) How many seconds after being thrown will the stone reach its maximum height? seconds

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) How many seconds after being thrown will the stone reach its maximum height? seconds

Bytelearn · Accepted Answer

Identify Function Type: Identify the type of function and its properties. The function w(x) = -5(x - 8)(x + 4) is a quadratic function in the form of w(x) = a(x - h)(x - k), where a is a negative constant, indicating that the parabola opens downwards. This means the vertex of the parabola represents the maximum height of the stone.Find Vertex x-coordinate: Find the x-coordinate of the vertex of the parabola. The x-coordinate of the vertex of a parabola in the form w(x) = a(x - h)(x - k) is the average of h and k. In this case, h = 8 and k = -4. So, the x-coordinate is (8 + (-4))/2 = 4/2 = 2.Determine Maximum Height Time: Determine the time when the stone reaches its maximum height. The x-coordinate of the vertex corresponds to the time in seconds when the stone reaches its maximum height. Therefore, the stone will reach its maximum height 2 seconds after being thrown.

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