Answer :
Answer:
[tex]y=x^2+6[/tex]
Step-by-step explanation:
Parent function:
[tex]y=x^2[/tex]
this is the parent function of a parabola (the simplest form of parabola).
To move this function vertically we use the following:
[tex]y=x^2+h[/tex]
where h is the amount of units we want to move this parabola, and we have the plus sign ([tex]+[/tex]) because we want to move it up (if you would like move it vertically but down, the sign should be negative -).
In this case, because we want to move it 6 units:
[tex]h=6[/tex]
and the function of the translated graph is
[tex]y=x^2+6[/tex]
The equation of function which have vertical translation by 6 unit will
[tex]f(x)=x^{2} +6[/tex]
To understand more, check below explanation.
Translation of function:
The equation of function is given as,
If we have to shift graph of function a unit down. then required equation will be, [tex]y=f(x)-a[/tex]
If we have to shift graph of function a unit up. then required equation will be, [tex]y=f(x)+a[/tex]
We have to translate parent function [tex]y=x^{2}[/tex] by 4 units vertically up
Hence, required equator will be [tex]y=x^{2} +6[/tex]
Learn more about the graph of function here:
brainly.com/question/24748644