Solve y=-1/2(x+1)^2-3

$$y = - \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 3$$

Solve for y

$$y=-\frac{x^{2}}{2}-x-\frac{7}{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$y=-\frac{1}{2}\left(x^{2}+2x+1\right)-3$$

Use the distributive property to multiply -\frac{1}{2} by x^{2}+2x+1.

$$y=-\frac{1}{2}x^{2}-x-\frac{1}{2}-3$$

Subtract 3 from -\frac{1}{2} to get -\frac{7}{2}.

$$y=-\frac{1}{2}x^{2}-x-\frac{7}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{-2y-6}-1$$

$$x=\sqrt{-2y-6}-1$$

Solve for x

$$x=-\sqrt{-2y-6}-1$$

$$x=\sqrt{-2y-6}-1\text{, }y\leq -3$$