3 equations, three unknowns
if they are co linear though, one equation will be a constant times another and there will be no unique solution.
show that; given any three non-collinear points (x1,y1), (x2,y2), (x3,y3) there is a parabola p(x)=Ax^2+ Bx + c , containing the three points.
3 answers
okay, i'm just not exactly sure where to start in trying to prove this though.
y = a x ^ 2 + b * x + c
You must solve system of equations :
a * x1 ^ 2 + b * x1 + c = y1
a * x2 ^ 2 + b * x2 + c = y2
a * x3 ^ 2 + b * x3 + c = y3
then put values of a , b and c in equation :
y = a x ^ 2 + b * x + c
You must solve system of equations :
a * x1 ^ 2 + b * x1 + c = y1
a * x2 ^ 2 + b * x2 + c = y2
a * x3 ^ 2 + b * x3 + c = y3
then put values of a , b and c in equation :
y = a x ^ 2 + b * x + c
1 answer