Answer
Vertex = (2, -1)
Step-by-step explanation
The general form of the parabola equation that shows the vertex of the parabola as (h, k) is
y = a (x - h)² + k
So, for this question, the parabola equation is
x² - 16y - 4x - 12 = 0
x² - 4x - 12 = 16y
We can rewrite this as
16y = x² - 4x - 12
Divide through by 16
y = (1/16) [x² - 4x - 12]
Completing the square of x² - 4x,
x² - 4x + (-4/2)² - (-4/2)²
= x² - 4x + 4 - 4
= (x - 2)² - 4
We can put this into the equation
y = (1/16) [x² - 4x - 12]
y = (1/16) [x² - 4x + 4 - 4 - 12]
y = (1/16) [(x - 2)² - 4 - 12]
y = (1/16) [(x - 2)² - 16]
y = [(1/16) (x - 2)²] - [(1/16) (16)]
y = (1/16) (x - 2)² - 1
Comparing this with
y = a (x - h)² + k
we can easily see that
a = (1/16)
h = 2
k = -1
Vertex = (h, k) = (2, -1)
Hope this Helps!!!