1. In general your approach to solve this question is OK:

If you want to use the equation of a parabola:

then you need the coordinates of three points of the parabola. You'll get a system of 3 simultaneous equations with 3 variables ((a,b,c)). Since you know 3 points of each parabola this way will lead to a valid solution. (You certainly noticed that (17, 14) is a point on the 2nd or 3rd parabola)

2. BUT: Since you know the vertex and at least one additional point it would be easier to use the vertex form of the equation of a parabola: If

is the vertex of a parabola it has the equation:

3. The equation of the 1st parabola is then:

. Plug in the coordinates (7, 14):

Therefore:

Expand the bracket and collect like terms:

4. The two other equations can be obtained in a similar way.