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

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

Solve for y

$$y=4x\left(x-2\right)$$

Solution Steps

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

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

Use the distributive property to multiply 4 by x^{2}-2x+1.

$$y=4x^{2}-8x+4-4$$

Subtract 4 from 4 to get 0.

$$y=4x^{2}-8x$$

Solve for x

$$x=-\frac{\sqrt{y+4}}{2}+1$$

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