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, y, in metres, at any time, x, in seconds.
To find the maximum height of the rocket, we need to find the vertex of the parabola represented by the equation y = -1/((x+6)(x-18)).
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -1, b = 0, and c = 0 (since there are no linear or constant terms in the equation).
So, x = -0/(2(-1)) = 0.
To find the y-coordinate of the vertex, we need to substitute x = 0 into the equation:
y = -1/((0+6)(0-18)) = -1/(-6)(18) = 1/108
Therefore, the maximum height of the rocket is 1/108 metres, or approximately 0.00926 metres or 9.26 millimetres.
Note: It's possible that the equation was meant to be y = -1/((x+6)(x-18)), with a negative sign in front of the whole fraction. In this case, the maximum height would still be 1/108 metres, but with a positive sign.