Solve y=left(x-1right)^2-4

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

Solve for y

$$y=\left(x-3\right)\left(x+1\right)$$

Solution Steps

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

$$y=x^{2}-2x+1-4$$

Subtract 4 from 1 to get -3.

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

Solve for x (complex solution)

$$x=-\sqrt{y+4}+1$$

$$x=\sqrt{y+4}+1$$

Solve for x

$$x=-\sqrt{y+4}+1$$

$$x=\sqrt{y+4}+1\text{, }y\geq -4$$