If you have 3 points of a parabola that are'nt the vertex and the only other information you recieve is that the A.O.S is parallel to the y axis how would you acurately find the equation? Everytime I try, I always end up with odd fractions......... the pts are (-3,-4),(adsbygoogle = window.adsbygoogle || []).push({});

(-1,-1), (2,3)

2. Relevant equations: general form: y=ax^2+ bx+c standard form: y-h=a(x-k)^2 a=1/4l l is the distance from the vertex to either the directrix or the focus, also that the equations opens either up or down....

Attempt:(-3,-4) -4=9a-3b+c (-1,-1) -1=a-b+c (2,3) 3=4a+2b+c

(-1)(-4=9a-3b-c) (-1)(-4=9a-3b-c)

(-1= a -b+c) (3=4a+2b+c)

+ ___________ +____________

3=-8a+2b 7=-5a+5b

(-5)(3=-8a+2b)

( 2)(7=-5a+5b)

+_____________

1=30a a=1/30

7=-5(1/30)+5b 7= -5/30+5b 215/30=5b 1075/30=b b= 215/6 a=1/30 b=215/6

3=4a+2b+c 3=4/30+2(215/6)+c 86/30= 215/3+c c=-2064/30

after that point: I thought something went wrong and attempted to redo it.........-.-

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# Homework Help: How to find the equation of a parabola with only 3 pts.

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