Respuesta :

carlosego
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
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


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