Answer:
Vertex coordinates; (h,k) = (2, -1)
Step-by-step explanation:
Vertex form of a parabola is;
y = a(x - h)² + k
Now, we are given;
x² - 16y - 4x - 12 = 0
Rearranging, we have;
x² - 4x = 16y + 12
Let's complete the square on the left hand side;
First add square of half of the coefficient of x to both sides;
x² - 4x + (-½ × 4)² = 16y + 12 + (-½ × 4)²
x² - 4x + 4 = 16y + 12 + 4
LHS can be expressed as;
(x - 2)² = 16y + 16
16y = (x - 2)² - 16
Divide both sides by 16 to get;
y = (1/16)(x - 2)² - 1
Comparing this with y = a(x - h)² + k, we have;
a = 1/16
h = 2
k = -1
(h,k) = (2, -1)
