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. How far horizontally from its starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point, will the rocket land? Round your answer to the nearest hundredth.

4.30 m
160.56 m
160.23 m
13.94 m

Question

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. How far horizontally from its starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point, will the rocket land? Round your answer to the nearest hundredth.

4.30 m
160.56 m 
160.23 m 
13.94 m

cloverracer · Answer

please help I have been waiting for an hour :((

anonymous · Answer

To find where the rocket lands, make y = 0
y = -.0.06x^2 + 9.6x + 5.4  = 0. This is a quadratic equation.Use the quadratic formula to get x.
Find D = b^2 - 4ac = 92,16 + 12.96 = 79.25 -> VD = 9.66
x = -b/2a + VD/2a = 9.6/0.12 + 9.67/0.12 = 160. 58

cloverracer · Answer

thank you!