SOLUTION: The 3 points (0,5), (1,3), (4,21) lie on a parabola and an inverse parabola. Find the two equations. I tired substituting in the points then using simultaneous equations to solv

Algebra ->  Graphs -> SOLUTION: The 3 points (0,5), (1,3), (4,21) lie on a parabola and an inverse parabola. Find the two equations. I tired substituting in the points then using simultaneous equations to solv      Log On


   

Question 919974: The 3 points (0,5), (1,3), (4,21) lie on a parabola and an inverse parabola. Find the two equations.
I tired substituting in the points then using simultaneous equations to solve but it didn't work...
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Parabola
y=ax%5E2%2Bbx%2Bc
.
.
.
1.5=a%280%29%2Bb%280%29%2Bc
1.c=5
.
.
.
2.3=a%281%29%2Bb%281%29%2B5
2.a%2Bb=-2
.
.
.
3.21=a%2816%29%2Bb%284%29%2B5
3.16a%2B4b=16
3.4a%2Bb=4
From eq. 2,
a=-2-b
Substituting,
4%28-2-b%29%2Bb=4
-8-4b%2Bb=4
-3b=12
b=-4
Then,
a=-2-%28-4%29
a=2
.
.
.
highlight_green%28y=2x%5E2-4x%2B5%29
.
.
.
Inverse parabola
x=ay%5E2%2Bby%2Bc
.
.
4.0=a%2825%29%2Bb%285%29%2Bc
4.25a%2B5b%2Bc=0
.
.
5.1=a%289%29%2Bb%283%29%2Bc
5.9a%2B3b%2Bc=1
.
.
6.4=a%28441%29%2Bb%2821%29%2Bc
6.441a%2B21b%2Bc=4
Subtract eq. 5 from eq. 4 and eq. 6 to eliminate c
7.25a%2B5b%2Bc-%289a%2B3b%2Bc%29=0-1
7.16a%2B2b=-1
.
.
8.441a%2B21b%2Bc-%289a%2B3b%2Bc%29=4-1
8.432a%2B18b=3
8.144a%2B6b=1
Multiply eq. 7 by -3 and add to eq. 8 to eliminate b
144a%2B6b-48a-6b=1%2B3
96a=4
a=1%2F24
Then,
16%281%2F24%29%2B2b=-1
2%2F3%2B2b=-1
2b=-5%2F3
b=-5%2F6
Finally,
9%2F24%2B3%28-5%2F6%29%2Bc=1
9%2F24-60%2F24%2Bc=24%2F24
c=75%2F24
c=25%2F8
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.
.
highlight_green%28x=y%5E2%2F24-%285%2F6%29y%2B25%2F8%29

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Fombitz beat me to it. I always like to show graphs, and
the tutors that just show the algebra and no graphs usually
beat me to it because I have to do the algebra first and
then do the graphs. Anyway here's the graph:

Edwin