Question

7. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the

equation y = .02x2 +9.5x + 5.6, 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? Round your answer to the nearest hundredth meter. Show all work.​

Answer 1

Answer: 475.59 meters .

Explanation:

The correct equation is the following:

`y =-0 .02x^2 +9.5x + 5.6`

For this exercise you need to use the Quadratic formula:

`x = (-b\±√(b^2-4ac))/(2a)`

In this case you can identify that the values of "a", "b" and "c" are:

`a=-0.02\\\\b=9.5\\\\c=5.6`

Now you must substitute these values into the Quadratic formula and then evaluate. You get:

`x=(-9.5\±√((9.5)^2-4(-0.02)(5.6)))/(2(-0.02))\\\\x_1=475.588\\x_2=-0.588`

Choose the positive one and round it to the nearest hundreth:

`x_1\approx 475.59`