The equation for a parabola has the form y = ax2 + bx + c, where a, b, and c are constants and a ≠ 0. Find an equation for the parabola that passes through the points (−1, −11), (1, −5), and (2, −8).

Putting (-1, -11) in given equation, we get :

-11 = a + -b + c    1)

Similarly putting (1, −5) and (2, −8) we get :

-5 = a + b + c      2)

-8 = 4a + 2b + c 3)Adding equation of 1) and 2) we get :

2( a + c ) = -6

a + c = -3

Solving equation 1 , 2 and 3 ,we get :

a = -2 , b = 3 , c = -6

Therefore, equation of parabola is :

y = -2x² + 3x -6

Hence, this is the required solution.

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