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The path of a toy rocket is defined by the relation y=-3x^2+11x+4, where x is the horizontal distance, in meters, traveled and y is the height, in metres, above the ground.
Determine the zeros of the relation.
-3x^2 + 11x + 4 = 0
3x^2 - 11x -4 = 0
3x^2 - 12x + x - 4 = 0
3x(x-4) + x-4 = 0
(x-4)(3x+1) = 0
x = 4 or x = -1/3
f(x) = -3x^2+11x+4
How far has the rocket traveled horizontally when it lands on the ground?
What is the maximum height of the rocket above the ground, to the nearest hundredth of a meter?
max occurs when x = -b/2a = -11/(2*-3) = 11/6
height = f(11/6) = 14.083 ft