Final answer:
The vertex form of a parabola with a vertex at (1, 5) is y = a(x - 1)² + 5, with 'a' being an undetermined coefficient that influences the direction and width of the parabola.
Step-by-step explanation:
The vertex form of a parabola is generally written as y = a(x - h)² + k, where (h, k) represents the vertex of the parabola and 'a' determines the direction and width of the parabola. If we have a vertex at (1, 5), we can substitute h and k into the vertex form, which gives us y = a(x - 1)² + 5.
To fully determine the vertex form, we would also need to know the value of 'a' which is typically derived from another point on the parabola or the direction of its opening. However, with only the vertex given, the vertex form can be written with 'a' as an undetermined coefficient, as shown above.