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 (−1,8), (2,−4), and (−6,−12).

The equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is .

Step-by-step explanation:

Let be (−1,8), (2,−4), and (−6,−12) points contained in a parabola, which is represented by a second-order polynomial. To determine the constant of the second-order polynomial, the following system of equations must be solved:

There are several methods for solving this: Equalization, Elimination, Substitution, Determinant and Matrix. The solution of this system is: , and . Hence, the equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is .

your answer would be 10x - 1