QUESTIONS - ANSWERS - EQUATIONS

QUESTIONS - ANSWERS - EQUATIONS
Find an equation of the form y = ax^2 + bx + c whose graph passes through the points (1,-2) (2,-1), and (3,4).
SUBSTITUTING THE VALUE OF X FROM POINTS(X,Y) IN THE GIVEN EQN. FOR Y WE GET
A+B+C=-2...................1
4A+2B+C=-1.......................2
9A+3B+C=4............3
EQN.2-EQN.1
3A+B=1................4
EQN.3-EQN.2
5A+B=5.................5
EQN.5 - EQN.4
2A=4
A=2
SUBSTITUTING IN EQN.4....
6+B=1
B=-5
SUBSTITUTING IN EQN.1
2-5+C=-2
C=1
HENCE THE EQN.IS
Y = 2X^2-5X+1