(1,-2),(-1,-4),(2,11)

Question

help solve

Answer 1

What is the question. These three points are not collinear (do not lie on the same straight line).

They could lie on a parabola y=ax²+bx+c:

(1) Plug in (1,-2): -2=a+b+c

(2) Plug in (-1,-4): -4=a-b+c

(3) Plug in (2,11): 11=4a+2b+c

We have three equations and three unknowns.

Subtract eqn (2) from eqn (1): 2=2b, so b=1.

Now plug b=1 into the other two eqns:

(2) becomes -4=a-1+c, so a+c=-3; (3) becomes 11=4a+2+c, so 4a+c=9.

Now we have two eqns:

a+c=-3

4a+c=9

Do this subtraction:

4a+c-(a+c)=9-(-3)=12,

3a=12, so a=4, therefore 4+c=-3, c=-7, and y=4x²+x-7.

All three points lie on this curve.