Find the height, in feet, of missile after 4 seconds in the air. A missile is launched from the ground. It’s height, h(x), can be repr

CPhill's answer is correct of course.  I am not going to do all of it all over again.  I just want to look at the beginning.

The trajectory is an upside down parabola.

I am going to let time be represented by t because x is used for distance and I think it is confusing (sorry)

Height can be h that is fine.

$$h(t)= -at^2+bt+c\qquad where\:\: a>0$$      

Already it looks different Cphill had a but his a was negative so my answer will work out the same.

I have used -a because I know the parabola is upside down (negative concavity)

NOW when time=0 height =0 therefore aber you substiture thesw values in you get c=0 so

$$h(t)= -at^2+bt\qquad where\:\: a>0$$

NOW it is the same as CPhill's so you can keep going from there.

This is modeled by.....

h(t) =  ax^2 + bx  

and

h(1) =  a(1)^2 + b(1) =  110  →     110 = a + b    (1)

and

h(2) =  a(2)^2 + b(2) =  200  →     200 = 4a + 2b   (2)

Multiplying (1) by -2 and adding it to (2) gives us

-20 = 2a       so   a = -10

And substituting this back into (1) we can find b

110= -10 + b       so b = 120

So our function is

h(t) = -10x^2 + 120x

So....after 4 seconds

h(4) =   -10(4)^2 + 120(4)  =  320 ft.