What is the vertex form of the equation of the parabola with a focus at (2,-13) and a directrix of y=23 ?

The equation of parabola is $y = - \frac{1}{72} {\left(x - 2\right)}^{2} + 5$
The vertex is at midway between focus$\left(2 , - 13\right)$and directrix $y = 23 \therefore$The vertex is at $2 , 5$ The parabola opens down and the equation is $y = - a {\left(x - 2\right)}^{2} + 5$ The vertex is at equidistance from focus and vertex and the distance is $d = 23 - 5 = 18$ we know $| a | = \frac{1}{4 \cdot d} \therefore a = \frac{1}{4 \cdot 18} = \frac{1}{72}$Hence the equation of parabola is $y = - \frac{1}{72} {\left(x - 2\right)}^{2} + 5$ graph{-1/72(x-2)^2+5 [-80, 80, -40, 40]}[Ans]