Given data:
The given expression is y= -1/2 (x+4)^2 +3.
The standard expression for the parabola is,
y=x^2
Shift the parabola by 4 units on y-axis.
y=(x^2 +4)
Then multiply with negattive sign, means the parabola is open downward.
y=-(x^2+4)
Mulltiply by 1/2 means the verrtical scale is reduced by 1/2 units.
y= -1/2 (x^2 +4)
Now add 3 units means the parabola shifts 3 units in vertical upward direction.
y= -1/2 (x^2 +4) +3.
The final parabola is open downward, passing (0,1).