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

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

Solve for y

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

Solution Steps

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

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

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

$$y=-2x^{2}-4x-2-3$$

Subtract 3 from -2 to get -5.

$$y=-2x^{2}-4x-5$$

Solve for x (complex solution)

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

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

Solve for x

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

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