# 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:

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

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