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Question

Write down an equation for a parabola that has a vertex at (4,2)

Answer 1

Vertex Form of a parabola:

y = a ( x - h)² + k

where vertex is: (h, k)

In this exercise, vertex is (4, 2), and assuming that a = 1:

h = 4

k = 2

a = 1

The equation of the parabola in Vertex Form is:

y = 1 (x - 4)² + 2

Answer 2

f(x) = a(x - 4)² + 2

Without an additional point a more specific equation is not possible.