What is the area, in sq. feet, of the debris?

[alyhandra3]

hello, I need to finish these questions by tomorrow for a project and I have no idea on how to do them due to my absences in the class because of illness. If anybody could provide help, that'd be greatly appreciated.

5. if the rockets collide at F, then the rockets will create a debris field that forms a parabola with vertex at F and scale factor of -1.5. Write the equation for parabola in y=ax^2=bx=c form.
(F as a vertex point is 927499.96478,359333.803

6. The parabola formed by the debris field is actually 3D. When a 3D parabola hits a plane like the land, then the intersection is a circle. What is the area, in sq. feet, of the debris?

Thanks for any and all help

 

[alyhandra3]

in regards to question 5 i misstyped some of the info..the equation is y=ax^2+bx+c..and the vertex is (27499.96478, 359333.803)

 

[HallsofIvy]

What you apparently missed from class is that the equation of a parabola, with vertical axis and vertex at (x₀,y₀), can be written y=a(x- x₀)²+ y₀. a is what you are calling the "scale" factor: -1.5 (negative because the parabola "opens" downward. Just plug the numbers you are given into that.

It's impossible to answer 6 because you haven't told us what the coordinates of the vertex MEAN. If we ASSUME that the y component is the height above the ground, then the debris will hit the ground when y=a(x- x₀)²+ y₀= 0. You don't really need to solve for x- what you want to know is x- x₀- how far away, horizontally, from the vertex the debris hit. That is the radius of the circle.