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

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

Solve for y

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

Solution Steps

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

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

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

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

Subtract 4 from 2 to get -2.

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y+8}}{2}+1$$

$$x=\frac{\sqrt{2y+8}}{2}+1$$

Solve for x

$$x=-\frac{\sqrt{2y+8}}{2}+1$$

$$x=\frac{\sqrt{2y+8}}{2}+1\text{, }y\geq -4$$