Translate f(x) = x^2 nine units right — find g(x) in the form a(x–h)^2+k

Step-by-step solution to translate f(x)=x^2 nine units to the right. Final answer given in the form a(x–h)^2+k with integer a, h, and k.

PDF

We start with f(x) = x2. A horizontal translation of a graph 9 units to the right is achieved by replacing x with (x - 9).

  1. Write g as the translated function: g(x) = f(x - 9).
  2. Substitute into f: g(x) = (x - 9)2.
  3. This is already in the form a(x – h)2 + k with a = 1, h = 9, k = 0.

Final answer:

g(x) = (x - 9)2

Ask a followup question