Solve y=-3(x-1)^2-4

$$y = - 3 ( x - 1 ) ^ { 2 } - 4$$

Solve for y

$$y=-3\left(x-1\right)^{2}-4$$

Solution Steps

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

$$y=-3\left(x^{2}-2x+1\right)-4$$

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

$$y=-3x^{2}+6x-3-4$$

Subtract 4 from -3 to get -7.

$$y=-3x^{2}+6x-7$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{-3y-12}}{3}+1$$

$$x=\frac{\sqrt{-3y-12}}{3}+1$$

Solve for x

$$x=-\frac{\sqrt{-3y-12}}{3}+1$$

$$x=\frac{\sqrt{-3y-12}}{3}+1\text{, }y\leq -4$$