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 + 10.1x + 5 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. 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 + 10.1x + 5 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 will the rocket land.
A.168.83m
B.5.00m
C.84.17m
D.430.04m

Answer 1

It's asking how far horizontally from the starting point which means that y, the height in meters is 0.
set 0 = -0.06x^2 + 10.1x + 5 and solve for x using the quadratic formula

-b +- $\sqrt{b^{2} -4ac}$ / 2a
-10.1 +- $\sqrt{10.1^2 - 4(-0.06)(5)$ / 2(-0.06)
you get that x = 168.83 m and -0.49 meters. Since the horizontal distance cant be negative, 168.83m is your answer