Question

Let f(x)=3x^2+5 . The quadratic function g(x) is f(x) translated 3 units up. Enter the equation for g(x) in the box. g(x) =

Answer 1

Answer:
`g(x)=3x^2+8`

Explanation:

There are some transformations for a function
`f(x)`. Two of those transformations are:

1. If
`f(x)+k`, then the function is translated "k" units up.

2. If
`f(x)-k`, then the function is translated "k" units down.

In this case, you have the following Quadratic function
`f(x)` given in the exercise:

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

According to the information given, the function
`g(x)` is obtained by translating the Quadratic function
`f(x)` 3 units up. Based on this, you can identify that the transformation is the following:

`f(x)+k`

Where
`k=3`

Therefore, you can determine that:

`g(x)=f(x)+3=3x^2+5+3\\\\g(x)=3x^2+8`