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

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

Solve for y

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

Solution Steps

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

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

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

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

Add 2 and 3 to get 5.

$$y=2x^{2}-4x+5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y-6}}{2}+1$$

$$x=\frac{\sqrt{2y-6}}{2}+1$$

Solve for x

$$x=-\frac{\sqrt{2y-6}}{2}+1$$

$$x=\frac{\sqrt{2y-6}}{2}+1\text{, }y\geq 3$$