Question

Which of the following equations is of a parabola with a vertex at (0, -5)?

y = (x - 5)2
y = (x + 5)2
y = x2 - 5
y = x2 + 5

Answer 1

Put 0 for x in each possible choice and see which one gives you y = -5.

The appropriate choice is
  y = x² - 5


_____
Of course, you know the vertex form is
  y = a(x -h)² + k
for vertex (h, k) and scale factor "a".
Then for (h, k) = (0, -5), this is
  y = ax² -5
Only one choice matches that: y = x² -5. (for a=1)

Answer 2

The equation
$y = {x}^{2} - 5$
will have a parabola with a vertex at (0,-5) as the y intercept is - 5. Remember, quadratic equations can often be written in the form
$y = a {x}^{2} + bx + c$
Where a is the coefficient of the quadratic, b is the coefficient of the multiple and C is the vertex/y-intercept.