Originally Posted by

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

If you want to use the equation of a parabola: $\displaystyle y = ax^2+bx+c$ 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 $\displaystyle V(x_V, y_V)$ is the vertex of a parabola it has the equation: $\displaystyle y = a(x-x_V)^2+y_V$

3. The equation of the 1st parabola is then: $\displaystyle y = a \left(x-\frac92\right)^2+\frac{81}4$. Plug in the coordinates (7, 14):

$\displaystyle 14 = a \left(7-\frac92\right)^2+\frac{81}4~\implies~a = -1$

Therefore: $\displaystyle y = (-1) \left(x-\frac92\right)^2+\frac{81}4$

Expand the bracket and collect like terms: $\displaystyle y = -x^2+9x$

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