Question

The graph of h is a translation 4 units right and 1 unit down of the graph of

f(x) = 3(x - 5)^2 - 1. Write an equation for h(x) in vertex form and explain how you reached your answer.

Answer 1

h(x) = 3(x - 9)² - 2

Explanation:

Rules for translation of a function are as follows:

f(x) + a = vertical translation of f(x) upwards by a units

f(x) - a = vertical translation of f(x) downwards by a units

f(x + a) = horizontal translation of f(x) leftwards by a units

f(x - a) = horizontal translation of f(x) rightwards by a units

So, using the above the rules:

h(x) = f(x - 4) - 1

h(x) = (3((x - 4) - 5)² - 1) - 1

h(x) = 3(x - 9)² - 2