Answer: [tex]g(x)=3x^2+8[/tex]
Step-by-step explanation:
There are some transformations for a function [tex]f(x)[/tex]. Two of those transformations are:
1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.
2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.
In this case, you have the following Quadratic function [tex]f(x)[/tex] given in the exercise:
[tex]f(x)=3x^2+5[/tex]
According to the information given, the function [tex]g(x)[/tex] is obtained by translating the Quadratic function [tex]f(x)[/tex] 3 units up. Based on this, you can identify that the transformation is the following:
[tex]f(x)+k[/tex]
Where [tex]k=3[/tex]
Therefore, you can determine that:
[tex]g(x)=f(x)+3=3x^2+5+3\\\\g(x)=3x^2+8[/tex]
