A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.06x² + 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 will the rocket land? Round your answer to the nearest hundredth.

Question

• 4.30 m
• 160.56 m
• 160.23 m
• 13.94 m
I know it is 160 but can't find which one --.56 or .23

Answer 1

Easy question. Put this in your google search window:

-.06*(160.23)^2 + 9.6*160.23)+5.4 =

does it equal zero? Verify by trying this:
-.06*(160.56)^2 + 9.6*160.56)+5.4 =

Answer 2

That did not help with the choices of .56 or .23
Any more help will be appreciated.

Answer 3

I get 160.56

just use the quadratic formula.

x = (-9.6 ±√(9.6^2 + 4(.06)(5.4)))/-.12
= (-9.6 ±√93.456)/-.12
= (-9.6 ±9.667)/-.12
= .067/-.12 or 19.267/.12
= -0.558 or 160.56

If you had plugged in bobpursley's data, you'd have seen that f(160.56) = 0.005, pretty close to zero.