c) Determine the equation of the axis of the symmetry group of students launching 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 meters, at any time, �, in seconds.
To determine the equation of the axis of symmetry of the rocket's height function, we need to find the x-value at which the height is maximized. This x-value corresponds to the axis of symmetry.
The height function given is:
y = -(x + 6)(x - 18)
To find the x-value at which the height is maximized, we can use the vertex formula. The vertex formula for a quadratic function of the form y = ax^2 + bx + c is given by:
x = -b / (2a)
In our case, the quadratic function is y = -(x + 6)(x - 18), which can be rewritten as y = -x^2 + 12x + 108.
Comparing this with the general form ax^2 + bx + c, we have a = -1, b = 12, and c = 108.
Using the vertex formula, we can calculate the x-value of the axis of symmetry:
x = -12 / (2(-1))
x = -12 / (-2)
x = 6
Therefore, the equation of the axis of symmetry for the rocket's height function is x = 6.