Quadratic function

Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4)

Final Answer:

a =  6
b =  -3
c =  1

Step-by-step explanation:

f(x) = a x2 + b x + c A=(−1,10) B=(2,19) C=(1,4)  a⋅ Ax2​+b⋅ Ax​+c=Ay​ a⋅ Bx2​+b⋅ Bx​+c=By​ a⋅ Cx2​+b⋅ Cx​+c=Cy​ a⋅ (−1)2+b⋅ (−1)+c=10 a⋅ 22+b⋅ 2+c=19 a⋅ 12+b⋅ 1+c=4  a−b+c=10 4a+2b+c=19 a+b+c=4  Pivot:Row1↔Row2  Row2−41​⋅ Row1→Row2 −1.5b+0.75c=5.25  Row3−41​⋅ Row1→Row3 0.5b+0.75c=−0.75  Row3−−1.50.5​⋅ Row2→Row3 c=1  b=−1.55.25−0.75c​=−1.55.25−0.75⋅ 1​=−3 a=419−2b−c​=419−2⋅ (−3)−1​=6  a=6 b=−3  f(x) = a x2 + b x + c f(x) = 6x2−3x+1

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