1. Use vertex form of quadratic equations f (x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
2. If the parabola is upside down remember to add in a negative in front of a.
3. Substitute the (x,y) coordinates of the vertex in the vertex form equation remember h=x and k=y.
4. Now, substitute any point (x,y) from the table into the x and f (x) of the vertex form, f (x)=y.
5. Solve for a.
6. Goto #3 and sub in the a value from step #5.
7. You are done and have a equation in vertex form.
To change to standard just distribute (a) value into the equation (distribution property) and simplify (add or subtract like terms).