Question

Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point.
A. Maximum at (2, –2)
B. Minimum at (2, –2)
C. Maximum at (2, 6)
D. Minimum at (2, 6)

Answer 1

Applying the completing square method:
f(x) = 2x² - 8x + 6
Dividing by a
f(x) = 2(x² - 4x + 3)
Adding and subtracting the square of b (which is 2 in this case)
f(x) = 2(x² + 2² - 4x -2²  + 3)
f(x) = 2(x - 2)² - 2
The vertex is (2, -2) and it is a minimum since the coefficient of x is positive.
The answer is B.