When x = 3, you get:
. . . . .-(4/9)[3]<sup>2</sup> + (24/9)[3] - 4
. . . . .-(4/9)[9] + (24/3) - 4
. . . . .-4 + 8 - 4
. . . . .0
...so the point (x, y) = (3, 0) is on this curve. Checking for the vertex:
. . . . .h = -b/(2a)
. . . . .= -(24/9) / (2(-4/9))
. . . . .= (-8/3) / (-8/9)
. . . . .= (-8/3)(-9/8)
. . . . .= 3
...so the point (3, 0) is the vertex, (h, k). Your equation would appear to be correct.
Eliz.