Find the values of ab and c such that the graph of the polyn

Find the values of a,b, and c such that the graph of the polynomial p(x)=ax²+bx+c passes through the points (1,1), (2,2) and (3,5).

Solution

p(x)=ax2+bx+c

plugging the values in the equation

(1,1)

1 = 1a+1b+c ----------------------- 1st equation

(2,2)

2 = 4a +2b + c -------------------2nd equation

(3,5)

5 = 9a + 3b + c ------------------- 3rd equation

on solving the 3 equations for a,b,c we get

a = 1

b = - 2

c = 2