I would approach this a little differently.
It is an absolute value equation, so its general form is: y - k = a|x - h|
where the vertex is located at the point (h, k) and its slope is a:
In function form, this becomes: f(x) = a|x - h| + k (notice the change-in-sign of the k-term)
For this problem, h = 6 and k = -1.
To find a, which is the slope, use the formula: (y2 - y1)/(x2 - x1).
We can use (0, 11) for (x1, y1) and (6, -1) for (x2, y2), so a = (-1 - 11)/(6 - 0) = -12/6 = -2.
However, being an absolute value graph, the slope will be negative if it opens downward, positive if it opens upward; so we have to change the -2 to a +2. (We got the negative because we used a point where the line fell downward to the vertex; if we used a point to the right of the vertex, where the line went upward, we would have gotten a +2.)
This makes our function: f(x) = 2|x - 6| - 1
Thus, a = 2 and b = 6.
