Answer:
4(x - 5)^2 - 18.
Step-by-step explanation:
For a move 5 to the right f(x) ----> f(x - 5).
For a move of 2 down f(x - 5) ----> f(x - 5) - 2.
For this case we have that by definition of function transformation is fulfilled:
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph[tex]y = f (x + h),[/tex] the graph moves h units to the left.
Let k> 0:
To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
So, we have the following function:
[tex]h (x) = 4x ^ 2-16[/tex]
5 units on the right:
[tex]h (x) = 4 (x-5) ^ 2-16[/tex]
2 units down
[tex]h (x) = 4 (x-5) ^ 2-16-2\\h (x) = 4 (x-5) ^ 2-18[/tex]
Answer:
[tex]h (x) = 4 (x-5) ^ 2-18[/tex]
