FX parabola

Determine the equation of the parabola going through the following co-ordinates (1;2), (-1;-2), and (2;7)

Correct answer:

y = x^2+2x-1

Step-by-step explanation:

A=(1,2) B=(−1,−2) C=(2,7)  y=f(x)=a⋅ x2+b⋅ x+c  Ay​=a⋅ Ax2​+b⋅ Ax​+c By​=a⋅ Bx2​+b⋅ Bx​+c Cy​=a⋅ Cx2​+b⋅ Cx​+c 2=a⋅ 12+b⋅ 1+c (−2)=a⋅ (−1)2+b⋅ (−1)+c 7=a⋅ 22+b⋅ 2+c  a+b+c=2 a−b+c=−2 4a+2b+c=7  Pivot:Row1↔Row3 4a+2b+c=7 a−b+c=−2 a+b+c=2  Row2−41​⋅ Row1→Row2 4a+2b+c=7 −1.5b+0.75c=−3.75 a+b+c=2  Row3−41​⋅ Row1→Row3 4a+2b+c=7 −1.5b+0.75c=−3.75 0.5b+0.75c=0.25  Row3−−1.50.5​⋅ Row2→Row3 4a+2b+c=7 −1.5b+0.75c=−3.75 c=−1  c=1−1​=−1 b=−1.5−3.75−0.75c​=−1.5−3.75−0.75⋅ (−1)​=2 a=47−2b−c​=47−2⋅ 2+1​=1  a=1 b=2 c=−1  y=x2+2x−1

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