SOLUTION: Derive a quadratic equation using the following points: (1, -4), (2, -5), (3, -10)

Question 766776: Derive a quadratic equation using the following points: (1, -4), (2, -5), (3, -10)
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
y = ax^2+bx+c
(1) (1, -4) -> -4=a+b+c ,
(2) (2, -5) -> -5= 4a+2b+c,
(3) (3, -10) -> -10=9a+3b+c

(2)-(1):
-5+4=4a-a+2b-b+c-c
-1=3a+b (or 3a+b=-1)
(3)-(1):
-6=8a+2b (or 4a+b=-3)

taking the difference of these 2 we get

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

and thus b=5
Now from (1):
-4=-2+5+c (so c=-7)

y=-2x^2+5x+-7

:)

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