Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by h(x)=-(x+1)(x-7) How many seconds after being thrown will the ball reach its maximum height? seconds

Question

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground),  x seconds after Amir threw it, is modeled by  h(x)=-(x+1)(x-7) How many seconds after being thrown will the ball reach its maximum height? seconds

Bytelearn · Accepted Answer

Identify Quadratic Function: The ball's height is modeled by the quadratic function h(x) = -(x+1)(x-7). To find the maximum height, we need to find the vertex of the parabola represented by this function.Find Axis of Symmetry: The quadratic function is in factored form. To find the vertex, we can find the axis of symmetry, which is the line x = -b/2a for a quadratic equation ax^2 + bx + c. However, we first need to expand the function to identify a, b, and c.Expand Function: Expanding the function h(x) = -(x+1)(x-7) gives us h(x) = -x^2 + 6x - 7.Identify Coefficients: Now that we have the expanded form, we can identify a = -1, b = 6, and c = -7. The axis of symmetry is x = -b/2a.Calculate Axis of Symmetry: Substitute a and b into the formula for the axis of symmetry: x = -6/(2*(-1)) = -6/(-2) = 3.Determine Maximum Height: The axis of symmetry x = 3 is the x-coordinate of the vertex, which means the ball reaches its maximum height 3 seconds after being thrown.

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