SOLUTION: Struggling on how to find an equation when only given these three coordinates: (4,-10), (11,5), (23,17) Seems like it should be a quadratic eq, but confused without any x or y

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Struggling on how to find an equation when only given these three coordinates: (4,-10), (11,5), (23,17) Seems like it should be a quadratic eq, but confused without any x or y       Log On


   

Question 999688: Struggling on how to find an equation when only given these three coordinates:
(4,-10), (11,5), (23,17)
Seems like it should be a quadratic eq, but confused without any x or y axis values.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You're going to have to slog through it.
Start with the general equation for a quadratic.
y=ax%5E2%2Bbx%2Bc
Use the points,
-10=a%284%29%5E2%2Bb%284%29%2Bc
1.16a%2B4b%2Bc=-10
.
.
5=a%2811%29%5E2%2Bb%2811%29%2Bc
2.121a%2B11b%2Bc=5
.
.
.
17=a%2823%29%5E2%2Bb%2823%29%2Bc
3.529a%2B23b%2Bc=17
.
.
.
The quickest way is to use Cramer's rule,
A=%28matrix%283%2C3%2C%0D%0A16%2C4%2C1%2C%0D%0A121%2C11%2C1%2C%0D%0A529%2C23%2C1%29%29
abs%28A%29=-1596
.
.
.
A%5Ba%5D=%28matrix%283%2C3%2C%0D%0A-10%2C4%2C1%2C%0D%0A5%2C11%2C1%2C%0D%0A17%2C23%2C1%29%29
abs%28A%5Ba%5D%29=96
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.
.

abs%28A%5Bb%5D%29-4860
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.
.

abs%28A%29=33864
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.
.
a=abs%28A%5Ba%5D%29%2Fabs%28A%29=-%2896%2F1596%29=-%288%2F133%29
b=abs%28A%5Bb%5D%29%2Fabs%28A%29=4860%2F1596=405%2F133
c=abs%28A%5Bc%5D%29%2Fabs%28A%29=-%2833864%2F1596%29=-%282822%2F133%29
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y=-%281%2F133%29%288x%5E2-405x%2B2822%29
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