College algebra word problem

Question

Complete the square and find the minimum value of the quadratic function.

(a)    y = 2x² − 4x − 9

Answer 1

2(x^2 -2x )-9 = 2(x^2 -2x +1) -9 -2 = 2(x-1)^2 - 11;

vertex at (1, -11)