Vertex #(4,-9)# Focus #(4,-35/4)# and directrix # y = - 37/4#

Explanation:

#y=(x^2-8x+16)-16+7 = (x-4)^2 -9 # Vertex is at #(4,-9)# Vertex is at equidistant from focus and directrix. d(distance) # = 1/4|a| = 1/(4*1)=1/4# Here a =1 comparing withe general equation #y=a(x-h)^2+k# so focus co-ordinate is at#(4,(-9+1/4))=(4, -35/4)# and directrix equation is #y=-9-1/4 or y=-37/4)# graph{x^2-8x+7 [-20, 20, -10, 10]}[Ans]