Let the graph of g be a translation 2 units right and 1 unit down 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 2 units right, and 1 unit down, vertex will move to (2,-1)

=> h = 2, k = -1

Hence g(x) = (x - 2)² - 1