Question

What value represents the vertical translation from the graph of the

(x+5)2+3?
0 -5
O-3

Answer 1

The value 3 represents the vertical translation upwards of
`f(x)` to
`g(x)`

Explanation:

The question is incomplete or missing data.

The correct question

What value represents the vertical translation from the graph of the parent function
`f(x) = x^2` to the graph of the function

`g(x) = (x + 5)^2 + 3`?

Given functions:

Parent function

`f(x) = x^2`

Translated function

`g(x) = (x + 5)^2 + 3`

Translation rules

For horizontal shift

`f(x)\rightarrow f(x+c)`

If
`c>0` the function shifts
`c` units to the left.

If
`c<0` the function shifts
`c` units to the right.

For vertical shift

`f(x)\rightarrow f(x)+c`

If
`c>0` the function shifts
`c` units to the up.

If
`c<0` the function shifts
`c` units to the down.

From the functions given the translation rule can be given as:

`f(x)\rightarrow f(x+5)+3`

`g(x)=f(x+5)+3`

This shows the graph is shifted left by 5 units and upwards by 3 units.

Thus the value 3 represents the vertical translation of
`f(x)` to
`g(x)`