What is the vertex form of the equation of the parabola with a focus at (7,4) and a directrix of y=3 ?

The equation of Parabola is $y = \frac{1}{2} {\left(x - 7\right)}^{2} + \frac{7}{2}$
The vertex is at mid point between focus and directrix so vertex is at $\left(7 , 3.5\right)$. The equaton of parabola in vertex form is $y = a {\left(x - h\right)}^{2} + k \mathmr{and} y = a {\left(x - 7\right)}^{2} + 3.5$ The distance of vertex from directrix is 0.5 ; :. a=1/(4*0.5)=1/2So the equation is $y = \frac{1}{2} {\left(x - 7\right)}^{2} + \frac{7}{2}$ graph{1/2(x-7)^2+7/2 [-40, 40, -20, 20]}