d) Determine the maximum height of the rocket
A group of students launches a model rocket from the top of a building. The
students have determined the equation y = − ;
(x+ 6)(x− 18) to describe the
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height of the rocket above ground level, �, in metres, at any time, �, in seconds.
To determine the maximum height of the rocket, we need to find the vertex of the parabolic function described by the given equation.
The vertex of a parabola with equation y = ax^2 + bx + c is given by the coordinates (-b/2a, c - b^2/4a). In this case, we have y = -1/((x+6)(x-18)), which can be rewritten as y = -1/(x^2 - 12x - 108).
Comparing this to the standard form of a parabolic function, y = ax^2 + bx + c, we see that a = -1, b = -12, and c = -108. Therefore, the x-coordinate of the vertex is x = -b/2a = 6, and the y-coordinate is y = c - b^2/4a = -9.
So the maximum height of the rocket is 9 meters above ground level.