Question

a parabola passes through the points (1,1) , (2,0) and (3,1)

the equation of the parabola is y=ax^2 + bx + c

a) write down a system of equations representing this parabola.

b) solve the corresponding system and hence write down the equation of the parabola

Answer 1

When x = 2, y = 0. Therefore, x = 2 is a solution. I'm going to derive the Eq
with the assumption that 2 is the only
solution. If my assumption is correct,
all given points will satisfy the derived Eq.

x = 2,
x - 2 =0,
(x - 2)^2 = x^2 - 4x + 4 = 0.

CHECK:
F(2) = 2^2 - 4*2 + 4 = 0, (2 , 0).
F(1) = 1^2 - 4*1 + 4 = 1, (1 , 1).
F(3) = 3^2 - 4*3 + 4 = 1, (3 , 1).