Answer:
The equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].
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:
[tex]a - b+c = 8[/tex]
[tex]4\cdot a +2\cdot b +c = -4[/tex]
[tex]36\cdot a -6\cdot b +c = -12[/tex]
There are several methods for solving this: Equalization, Elimination, Substitution, Determinant and Matrix. The solution of this system is: [tex]a = -1[/tex], [tex]b = -3[/tex] and [tex]c = 6[/tex]. Hence, the equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].
