Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1. (2 points) a. f(x) = − one twelfth (x − 5)2 + 2 b. f(x) = one twelfth (x − 5)2 + 2 c. f(x) = − one twelfth (x + 5)2 + 2 d. f(x) = one twelfth (x + 5)2 + 2

The focus is above the directrix, so the parabola opens upward—its vertical scale factor is positive (+1/12). The line of symmetry is x=-5, so the vertex form of the equation will have the factor (x -(-5))² = (x+5)². The choice that meets both these requirements is
  D. f(x) = (1/12)(x + 5)² + 2