Explanation:
the general vertex form is
y = a(x - h)² + k
with (h, k) being the vertex of the curve.
after doing all the multiplications we get
y = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k
now we have
y = x² + 24x + 124
and we can compare
ax² = x²
a = 1
-2ahx = -2hx = 24x
-2h = 24
h = 24/-2 = -12
ah² + k = 124
(-12)² + k = 124
144 + k = 124
k = -20
so, the vertex form is
y = (x + 12)² - 20