Question

answer this question or else answer this question or else answer this question or else answer this question or else answer this question or else
answer this question or else answer this question or else answer this question or else

Find g(x), where g(x) is the translation 16 units up of f(x) = -4|x + 5| - 10

write your answer in the form a|x - h| + k, where a, h, and k are integers

Answer 1

To find the function \( g(x) \) that represents the translation of \( f(x) = -4|x + 5| - 10 \) 16 units upward, we need to add 16 to the original function.

Starting with the original function:

\[
f(x) = -4|x + 5| - 10
\]

We translate it 16 units up:

\[
g(x) = f(x) + 16
\]

Substituting \( f(x) \):

\[
g(x) = (-4|x + 5| - 10) + 16
\]

Now simplifying the equation:

\[
g(x) = -4|x + 5| - 10 + 16
\]
\[
g(x) = -4|x + 5| + 6
\]

Next, we want to write \( g(x) \) in the form \( a|x - h| + k \). We can do this by rewriting \( |x + 5| \) as \( |x - (-5)| \):

Thus:

\[
g(x) = -4|x - (-5)| + 6
\]

So, we have:

- \( a = -4 \)
- \( h = -5 \)
- \( k = 6 \)

Therefore, the final form of \( g(x) \) is:

\[
g(x) = -4|x + 5| + 6
\]