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

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 

:)