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) What is the maximum height that the ball will reach? meters

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) What is the maximum height that the ball will reach? meters

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Understand Problem:  Understand the problem and identify the type of function. The function h(x) = -(x+1)(x-7) is a quadratic function, which opens downwards because the leading coefficient (the coefficient of x^2) is negative. This means the vertex of the parabola represents the maximum height of the ball. Convert to Standard Form:  Convert the function into standard form. To find the vertex more easily, we first convert the function into standard form, which is ax^2 + bx + c.  h(x) = -(x^2 - 7x + x - 7) = -x^2 + 6x + 7. Find x-coordinate of Vertex:  Find the x-coordinate of the vertex. The x-coordinate of the vertex of a parabola given by ax^2 + bx + c is found using the formula -b/(2a). Here, a = -1 and b = 6. x = -6/(2*(-1)) = 3. Find y-coordinate of Vertex:  Find the y-coordinate of the vertex. To find the maximum height, substitute x = 3 into the original equation. h(3) = -(3+1)(3-7) = -4*(-4) = 16. Conclude Maximum Height:  Conclude with the maximum height. The maximum height that the ball will reach is 16 meters.

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 $\newline$ $h(x) = -(x+1)(x-7)$ $\newline$ What is the maximum height that the ball will reach? $\newline$ $meters$

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