- #1
redretro
- 3
- 0
If you have 3 points of a parabola that are'nt the vertex and the only other information you receive 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),
(-1,-1), (2,3)
2. Homework 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...-.-
(-1,-1), (2,3)
2. Homework 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...-.-
