Parabola

Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)

Result

a =  0
b =  0
c =  0

Solution:

 a (6)2+b (6)+c=5 a (14)2+b (14)+c=9 a (23)2+b (23)+c=6  36a+6b+c=5 196a+14b+c=9 529a+23b+c=6  a=252040.122549 =0 b=8572044.20098 c=8773425.794118  \ \\ a \cdot \ (6)^2 + b \cdot \ (6) + c=-5 \ \\ a \cdot \ (14)^2 + b \cdot \ (14) + c=9 \ \\ a \cdot \ (23)^2 + b \cdot \ (23) + c=6 \ \\ \ \\ 36a+6b+c=-5 \ \\ 196a+14b+c=9 \ \\ 529a+23b+c=6 \ \\ \ \\ a=\dfrac{ -25 }{ 204 } \doteq -0.122549 \ \\ =0 \ \\ b=\dfrac{ 857 }{ 204 } \doteq 4.20098 \ \\ c=\dfrac{ -877 }{ 34 } \doteq -25.794118 \ \\
b=0b=0
c=0  f(x)=y=a x2+b x+cc=0 \ \\ \ \\ f(x)=y=a \cdot \ x^2+b \cdot \ x + c



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