Question

Describe the translation y=x^2+5

Answer 1

`y = {x}^(2) + 5`

EXPLANATION

The given function is

`y = {x}^(2) + 5`

The base of this function is

`f(x) = {x}^(2)`

The translation is of the form.

`y = f(x) + k`

where k is a vertical translation k units up.

`y = {x}^(2) + 5`

Therefore the translation is a shift up by 5 units.

Answer 2

The transformation moves the graph of the function up 5 units

Explanation:

If we have a function f(x) then the transformation

`g (x) = f (x) + c` vertically shifts the graph of f(x) c units

If
`c> 0` the graph moves c units up

If
`c <0` the graph moves c units down

In this case the main function is
`f (x) = x ^ 2`

and
`g (x) = f (x) + 5 = x ^ 2 +5`

Therefore the transformation moves the graph of the function up 5 units