Question

Consider the parent graph f(x) = x2 . Then, g(x) is a translation according the rule: y = (x + 3)2 + 4. Find the graph g(x).

Answer 1

For this case we have the following parent function:
 f (x) = x ^ 2
 We apply the following function transformation:
 Horizontal translations
 Suppose that h> 0
 To graph y = f (x + h), move the graph of h units to the left.
 We have then:
 y = (x + 3) ^ 2
 Vertical translations
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 We have then:
 y = (x + 3) ^ 2 + 4
 Answer:
 The graph g (x) is the graph f (x) 3 units to the left and 4 units up:
 y = (x + 3) ^ 2 + 4