I happened to speak with Mr S this afternoon and he made some comments about the Sheriff of Nottingham task that I think you should be aware of. He is expecting you to estimate the second zero (if you decide to use factored form) or the vertex* (if you use vertex form) and then to find a by using a data point (the position of Prince John). You will then need to check that you (a) clear the wall and (b) hit the target within a reasonably range of error (ie to the nearest metre).
There are other methods, and as long as they find the function, show that the wall is cleared and check that the target is hit, I will allow them. One analytical method is to choose another data point in addition to the known ones (0, 0) and (130, 10), and construct a system of three equations that you can solve simultaneously. The third data point would probably be something like (110, 60), ensuring that you clear the wall. This is very precise, but harder work. If you do it this way I will buy you the item of confectionery of your choice.**
* Don’t forget that if you know where both zeroes are, you can calculate the vertex, and if you know one zero and the vertex, you can calculate the other zero easily.
** Up to the value of 50PhP. Offer only open to my classes. Terms and conditions apply.