A missle is launched from the ground. Its height h(x), can be represented by a quadratic function in terms of time, x, in seconds. After 1 second, the missle is 130 feet in the air; after 2 seconds it is 240 feet in the air. Find the height, in feet, of the missle after 11 seconds in the air.

Question

whpalmer4 · Answer

Personally, I think t is a better letter for time than x :-)

$$h(t) = at^2 + bt + c$$
$$h(0) = 0$$$$h(1) = 130$$$$h(2) = 240$$
So now write the 3 equations you can form from this information and solve for the values of a, b, and c.

anonymous · Answer

@whpalmer4 Thats what I dont understand... how to plug then into an equation.

whpalmer4 · Answer

at t=0:
$$h(t) = 0 = a(0)^2 + b(0) + c \rightarrow c = 0
$$
at t=1:
$$h(t) = 130 = a(1)^2 + b(1) + 0 = a + b$$
at t=2:
$$h(t) = 240 = a(2)^2 + b(2) + 0 = 4a + 2b$$
That gives us 2 equations in 2 unknowns:
$$a + b = 130$$$$4a+2b = 240$$

Can you solve that?

anonymous · Answer

Got it! I'll solve it. thanks

whpalmer4 · Answer

Let me know what you get.

whpalmer4 · Answer

I had to do it twice, because I accidentally wrote 260 instead of 240 :-)