Solve y=4left(x-3right)^2-4

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

Solve for y

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$y=4\left(x^{2}-6x+9\right)-4$$

Use the distributive property to multiply 4 by x^{2}-6x+9.

$$y=4x^{2}-24x+36-4$$

Subtract 4 from 36 to get 32.

$$y=4x^{2}-24x+32$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{y+4}}{2}+3$$

$$x=\frac{\sqrt{y+4}}{2}+3$$

Solve for x

$$x=-\frac{\sqrt{y+4}}{2}+3$$

$$x=\frac{\sqrt{y+4}}{2}+3\text{, }y\geq -4$$