y = (x-4)(x+20) ===> 0 = (x-4)(x+20)
that means the roots of that quadratic are x = 4 and x = -20.
now, the vertex will be between these two guys, right in between.
from -20 to 4 there are 24 units, half-way of that is 12 units, so, if we move from -20, 12 units to the right or towards 4, we'll end up at -20 + 12 = -8.
so, the vertex's x-coordinate is -8 then, what's "y" anyway?
y = (x-4)(x+20) x = -8
y = [(-8) - 4] [(-8) + 20]
y = (-12) ( 12)
y = -144
therefore, the vertex is at (-8 , -144)