Question

Hey can you please help me posted picture of question

Answer 1

4x² - 16

5 units to right means subtracting 5 from the value of x. So the function will be:

4(x-5)² - 16

2 units down means subtracting 2 from the entire function.

So, the expression will be

4(x-5)² - 16 - 2
=4(x-5)² - 18

The above expression gives the equation after both the given translations have been applied.

So, the correct answer is option C

Answer 2

We have the following function:
f (x) = 4x ^ 2 - 16
Horizontal translations
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
We have then:
f (x) = 4 (x-5) ^ 2 - 16
Then,
Vertical translations
Suppose that k> 0
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 4 (x-5) ^ 2 - 16 - 2
f (x) = 4 (x-5) ^ 2 - 18
Answer:
f (x) = 4 (x-5) ^ 2 - 18
option C