Let the graph of g be a translation up 5 units of the graph of f(x)= x^2

Question

Write a new function rule for g(x)

Answer 1

Vertex form of a parabola is y = a(x−h)² + k with vertex at (h, k).

f(x) = x²

in which case, a = 1, h = 0, k = 0 and vertex must be at (0,0)

For translation 5 units up only, vertex will move to (0, 5)

=> h = 0, k = 5

Hence g(x) = x² + 5