Asked by Chelsea
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.
Answers
Answered by
Damon
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.
if they are co linear though, one equation will be a constant times another and there will be no unique solution.
Answered by
Chelsea
okay, i'm just not exactly sure where to start in trying to prove this though.
Answered by
Bosnian
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
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