Question

What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x + 5)2 + 3?

Answer 1

f (x) = x²

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left:

For h = 5 we have:

f (x+5) = (x+5)²

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

For k = 3 we have:

g(x) = (x+5)² + 3

The value which is represented by the vertical translation from the graph of parent function is 3

Answer 2

For this case we have that the parent capacities are given by:

We apply the accompanying capacity changes:

Horizontal interpretations:

Suppose that h> 0 To chart y = f (x + h), move the diagram of h units to one side:

For h = 5 we have:

Vertical interpretations:

Suppose that k> 0 To diagram y = f (x) + k, move the chart of k units up.