Parabola

Find the equation of a parabola that contains the points at A[10; -5], B[18; -7], C[20; 0]. (use y = ax2+bx+c)

Correct answer:

a =  0.375
b =  -10.75
c =  65

Step-by-step explanation:

f(x) = ax2​+bx​+c=y  a⋅ 102+b⋅ (10)+c=−5 a⋅ 182+b⋅ (18)+c=−7 a⋅ 202+b⋅ (20)+c=0  100a+10b+c=−5 324a+18b+c=−7 400a+20b+c=0  Pivot:Row1↔Row3 400a+20b+c=0 324a+18b+c=−7 100a+10b+c=−5  Row2−400324​⋅ Row1→Row2 400a+20b+c=0 1.8b+0.19c=−7 100a+10b+c=−5  Row3−400100​⋅ Row1→Row3 400a+20b+c=0 1.8b+0.19c=−7 5b+0.75c=−5  Pivot:Row2↔Row3 400a+20b+c=0 5b+0.75c=−5 1.8b+0.19c=−7  Row3−51.8​⋅ Row2→Row3 400a+20b+c=0 5b+0.75c=−5 −0.08c=−5.2  c=−0.08−5.2​=65 b=5−5−0.75c​=5−5−0.75⋅ 65​=−10.75 a=4000−20b−c​=4000−20⋅ (−10.75)−65​=0.375  a=83​=0.375 b=4−43​=−10.75 c=65
b=(−10.75)=−10.75
c=65  f(x) = y = a ⋅  x2+b ⋅  x + c

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