+129852 y = -(1/6)x^2 + 7x - 80 factor out the -1/6
y = -(1/6) [ x^2 - 42x + 480 ] complete the square on x
y = -(1/6) [ x^2 - 42x + 441 + 480 - 441 ]
y = -(1/6) [ ( x - 21)^2 + 39 ]
y = (-1/6)(x - 21)^2 - 39/6
(y +39/6) = (-1/6) (x - 21)^2 multiply both sides by -6
-6(y + 39/6) = ( x - 21)^2
-6 ( y + 6.5) = (x - 21)^2
4p = -6
p = -6/4 = -3/2
The vertex is ( 21, -6.5)
The directrix is given by : y = -6.5 - p = -6.5 - (-3/2) = -5
