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

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

Solve for y

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

Solution Steps

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

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

Use the distributive property to multiply -3 by x^{2}-2x+1.

$$y=-3x^{2}+6x-3-2$$

Subtract 2 from -3 to get -5.

$$y=-3x^{2}+6x-5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{-3y-6}}{3}+1$$

$$x=\frac{\sqrt{-3y-6}}{3}+1$$

Solve for x

$$x=-\frac{\sqrt{-3y-6}}{3}+1$$

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