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 equals -0.04 ^ 2 + 8.3 x + 4.3 where X is the horizontal distance in meters from the starting point on the roof and why 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

Answer 1

208.02 m

Explanation:

When the model rocket lands, y = 0; therefore, the equation becomes

`-0.04x^2+8.3x+4.3=0`

Using the quadratic formula we solve for x.

`x=\frac{-8.3\pm\sqrt[]{8.3^2-4(-0.04)(4.3)}}{2(-0.04)}`

Which simplifies to give

`x=\frac{-8.3\pm\sqrt[]{69.578}}{(-0.08)}`

Hence, we have the solutions

`\begin{gathered} x=208.02 \\ x=-0.52 \end{gathered}`

since lengths cannot be negative, we choose x = 208.02 as our answer.

Hence, the model rocket lands 208.02 m from the starting point.