Answer:
Shifted 3 units upwards.
Step-by-step explanation:
We have been given a parent function [tex]f(x)=x^2[/tex] and a translated function [tex]f(x)=(x+5)^2+3[/tex]. We are asked to determine the vertical translation from the parent function to [tex]f(x)=(x+5)^2+3[/tex].
Let us recall translation rules.
Horizontal translation:
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
Vertical translation:
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
Upon looking at our given function, we can see that the value of 'a' is positive 5 inside parenthesis, so our graph is shifted to left by 5 units.
We can also see that the value of 'a' outside parenthesis is positive 3, therefore, the graph of parent function is shifted upwards by 3 units to get the graph of function [tex]f(x)=(x+5)^2+3[/tex].
