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April 12th, 2017, 02:30 PM  #1 
Newbie Joined: Mar 2017 From: leuven Posts: 18 Thanks: 0  Making a function with the domain and top.
5. An object is shot upwards vertically under influence of gravity it shall slow down, after 3 seconds it reaches a highest point and it will fall down with an ever increasing speed. The maximum height is 20m a) Find the equation of the parabola trajectory in a self picked coordinate system. So basicly what i got out of this is that i need to build up the function or f(x) = based upon this data. What i know is that the object is launched at (0,0) reaches a top at (3,20) As it describes an object in the air that falls down i assume its a function of the second grade with the form: ax²6bx+c With a being <0 since the top is also the center of symetry in a second grade function it's easy to asume that it lands on the ground at (6,0) So briefly put: Code: startpoint: (0.0) max(3,20) endpoint:( 0.6) form: ax²+bx+c with a<0 I tried doing 20/3 since it takes 3 steps to reach 20 for a but simply doing that isn't enough i think. (Also sorry if something is unclear, i had to transelate this to english, my textbook is in dutch. and i don't know alot of the english names for matimatical terms) 
April 12th, 2017, 02:49 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,290 Thanks: 664 
after a brilliant start you just fizzled right out you have the form $y = a x^2 + b x + c$ you have 3 points on this curve $(0,0), ~(3,20),~(6,0)$ plug those points in and get a set of equations for $a,b,c$ solve the equations, they'll be linear in $a,b,c$ 
April 12th, 2017, 03:03 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,595 Thanks: 1285 
vertex form for the equation of a parabola ... $y = a(xh)^2 + k$, where the vertex is $(h,k)$ height is a function of time & you have the vertex coordinates, $(3,20)$ ... $h = a(t  3)^2 + 20$ use either $(0,0)$ or $(6,0)$ to determine the value of $a$ 
April 13th, 2017, 01:22 AM  #4  
Newbie Joined: Mar 2017 From: leuven Posts: 18 Thanks: 0  Quote:
Woa i had never heard of that so called vertex equation of a parabola, Good to know that that excists for future excercises. h= x(03)²+20 x*9+20=0 9x+20=0 9x=20 x=20/9= 2.2222.... so f(x)= 2.22222..(x3)²+20 i tested this on my calculator and it is indeed correct! always excited when i learn something new.  
April 13th, 2017, 02:21 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,595 Thanks: 1285 
Put away the calculator. Recommend you leave the coefficient, $a$, in its exact form as a fraction. 
April 13th, 2017, 07:31 AM  #6 
Newbie Joined: Mar 2017 From: leuven Posts: 18 Thanks: 0  

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