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. How far horizontally from its starting point will the rocket land?
a:168.83
b:5.00
c:84.17
d:430.04

Answer 1

When the rocket hits the ground, its height will be zero.

Thus, set y = -0.06x^2 + 10.1x + 5 equal to zero and solve for x:

-0.06x^2 + 10.1x + 5 = 0

To remove the decimal fractions, divide all 4 terms by -0.06:

x^2 - 168.333x - 83.333 = 0

Alternatively, apply the quadratic formula:

a= -0.06, b= 10.1, c = 5
                                -10.1 plus or minus sqrt( 10.1^2 - 4(-0.06)(5) )
The formula is  x = ------------------------------------------------------------------
                                                              -0.12

Evaluate this to obtain the suitable value of x.  Note that this x must be positive, since it represents the measure of distance.