What is the axis of symmetry of the parabola...?

Take the general form of the parabola:
y = ax² + bx + c

The line of symmetry is:
x = -b/(2a)

If you need help remembering that, it's the same as the quadratic formula but without the ±√ part.

In your case:
a = 1
b = -4

x = -(-4) / (2*1)
x = 4/2
x = 2

Answer:
C. x = 2

Complete the square.
y = x^2 - 4x - 5
y = x^2 - 4x + 4 - 9
y = (x - 2)^2 - 9
axis of symmetry is x = 2

  What is the axis of symmetry of the parabola y = x^2 - 4x - 5?
  y = (x - 5)(x + 1)

  C    x = 2

Do you want the short answer or the long answer.

Short answer
Graph it and look for yourself
x = 2

long answer
take derivative
f'(x) = 2 x - 4

set to 0 and solve for x

0 = 2x - 4
4 = 2x
2 = x