Please help. The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation. The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff. The rocket touches the ground at a horizontal distance of 9 feet from the cliff. Determine a quadratic function that models the height h(d) of the rocket at any given distance d feet from the cliff.

Question

Please help.  The trajectory of a rocket launched from the top of a cliff can be modeled by a quadratic equation.  The rocket reaches a maximum height of 250 feet at a horizontal distance of 4 feet from the cliff.  The rocket touches the ground at a horizontal distance of 9 feet from the cliff.  Determine a quadratic function that models the height h(d) of the rocket at any given distance d feet from the cliff.

zzr0ck3r · Answer

so the height is the vertex
we use "vertex form"
$$y=a(x-h)^2+k$$
where the vertex is (h,k)
we know a<0 because it opens downward$$y=-a(x-4)^2+250$$
one of the zeros is (9,0)
so use that point to solve for a
$$0=-a25+250\a25=250\a=10$$so$$y=-10(x-4)^2+250$$

anonymous · Answer

Thank you so much!

zzr0ck3r · Answer

np

zzr0ck3r · Answer

my explanation got a little weird
I say that a<0 and then i write -a
I should have said if we consider a to be positive then we will have -a

but we could have just said a and solved and we would have got -10, so either way....