The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].
We need the knowledge of three distinct points to determine all coefficients of the vertical parabola based on the following general formula:
[tex]x^{2} + y^{2} + D\cdot x + E\cdot y + F = 0[/tex] (1)
If we know that [tex](x_{1}, y_{1}) = (-2, -18)[/tex], [tex](x_{2}, y_{2}) = (3,-13)[/tex] and [tex](x_{3}, y_{3}) = (5,-39)[/tex], then we have the following system of linear equations:
[tex]-2\cdot D -18\cdot E + F = -328[/tex] (2)
[tex]3\cdot D -13\cdot y + F = -178[/tex] (3)
[tex]5\cdot D -39\cdot E + F = -1546[/tex] (4)
The solution of the system of equations is: [tex]D = -21[/tex], [tex]E = 51[/tex], [tex]F = 548[/tex].
The general formula for the parabola is [tex]x^{2}+y^{2}-21\cdot x +51\cdot y +548 = 0[/tex].
We kindly invite to check this question on parabolae: https://brainly.com/question/4074088
