Answer:
B
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant.
Using the distance formula
= | y - 6 |
Squaring both sides
(x + 2)² + (y - 4)² = (y - 6)² ← distributing
x² + 4x + 4 + y² - 8y + 16 = y² - 12y + 36 ( subtract y² - 12y + 36 from both sides )
x² + 4x + 4 + 4y - 20 = 0 ( subtract x² + 4x + 4 from both sides )
4y - 20 = - x² - 4x - 4 ( add 20 to both sides )
4y = - x² - 4x + 16 ( divide through by 4 )
y = - x² - x + 4, that is
f(x) = - x² - x + 4 → B