Question 1200542
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<font color=red>Answer:</font> {{{y = sqrt(2x+10)+3}}}


Work Shown:
{{{y = sqrt(2x)}}}


{{{y = sqrt(2(x+5))}}} 


{{{y = sqrt(2(x+5))+3}}}


{{{y = sqrt(2x+10)+3}}}


Explanation:
The translation vector is (-5,3). 
It means "shift 5 units left and 3 units up"
In the 2nd step shown above, we replace x with (x+5) to shift 5 units to the left.
In the 3rd step, the +3 at the end shifts the entire curve up 3 units.


Graph
{{{
graph(400,400,-7,3,-3,7,sqrt(2x),sqrt(2(x+5)),sqrt(2(x+5))+3
)}}}
{{{y = sqrt(2x)}}} in red
{{{y = sqrt(2(x+5))}}} in green  (shift 5 units left)
{{{y = sqrt(2(x+5))+3}}} in blue (shifted 3 units up)


Desmos and GeoGebra are two graphing options I recommend.
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