The equation can be factored as (2x - 3)(2x - 3) = 0, hence the roots are 3 and 3.

Factoring gives (x - 3)(x - 7) = 0, so the roots are 3 and 7.

The sum of the roots is given by -b/a = 8/2 = 4.

Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.

The product of the roots is given by c/a = 9/3 = 3.

Using Vieta's formulas, the product of the roots is c/a = 10/1 = 10.

The discriminant D = b^2 - 4ac = 12^2 - 4*3*9 = 0, indicating equal roots.

The discriminant is b^2 - 4ac = 6^2 - 4(3)(2) = 36 - 24 = 12.

The vertex can be found using x = -b/(2a). Here, x = 12/(2*3) = 2. Substituting x = 2 into the equation gives y = 3(2)^2 - 12(2) + 7 = -5.

The vertex can be found using x = -b/(2a). Here, x = 8/(2*2) = 2. Substituting x = 2 into f(x) gives f(2) = -3, so the vertex is (2, -3).