A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.06x^2+9.6x+5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.
To find the maximum height of the rocket, we need to find the vertex of the parabolic equation y=-0.06x^2+9.6x+5.4.
The x-coordinate of the vertex of a parabola given by the equation y=ax^2+bx+c is given by x=-b/(2a). In this case, a=-0.06 and b=9.6.
Therefore, x=-9.6/(2*(-0.06)) = 80
Plugging x=80 into the equation, we get:
y=-0.06(80)^2+9.6(80)+5.4 = 384
So, the rocket reaches a maximum height of 384 meters.