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Visualize a scene with a house standing tall in a vast, open field under a clear blue sky. The house has a red roof from where a green and white model rocket is being launched. It follows a parabolic path represented with dotted lines. The rocket is midway in its path, at the peak of its height, which is dynamically visualised. The height above the ground and the horizontal distance from its starting point are also indicated. The landing point in the field is subtly indicated with a faint mark, but the exact distance is not depicted. Remember, the image does not contain any text.

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.

it's 160.56

i wish i can give you the formula so you won't have to search for answers and just work it out yourself but idk how to put all the symbols and stuff here so. I'm sorry! Hope that helps!!

btw it's a quadratic formula so look up the quadratic formula and just fill that out then simplify to find your answer!! ^^

since you want the height horizontally from the starting height, and that height was 5.4 metres,

-.06x^2 + 9.6x + 5.4 = 5.4
the 5.4 drops out, so

x(-.06x + 9.6) = 0
x = 0 , the starting time
or
x = 9.6/.06 = 160

it will land after 160 m

Thank you but could it also be 160.56 m or 160.23 m?

undi is correct still in 2022

Also, an another hint is that since it's height it can NEVER be negative so just cross out the other x value. ^^

Thank you, @undi. Still correct today!!!!!!!!

stay weird fam

Nuxenoir

truu

a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y=-0.02x^2+2.3x+6, 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?