Question 937573
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{{{y^2=x}}}


Stretch by factor of 0.5 is not stretch but shrink.
HORIZONTAL "stretch" is {{{0.5y^2=x}}}, and you are interested in the upper branch.


Reflect in the y-axis,
{{{-(1/2)y^2=x}}}


Shift two units to the left,
{{{-(1/2)y^2=x+2}}}


Simplify this back into y as a function of x.
{{{y^2=-2x-4}}}
{{{highlight(y=sqrt(-2x-4))}}}
This is the upper branch of the function.
Clearly understand that the expression within the square root function is NOT a negative value.  You have a domain which relies on {{{-2x-4>=0}}},
{{{-4>=2x}}}
{{{-2>=x}}}------the domain.


Aside from that, you can still adjust the equation as {{{y=sqrt((-2)(x+2))}}}.