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: $g(x)=3x^2+8$

Step-by-step 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:

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