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

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

Solve for y

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$y=2\left(x^{2}-8x+16\right)+1$$

Use the distributive property to multiply 2 by x^{2}-8x+16.

$$y=2x^{2}-16x+32+1$$

Add 32 and 1 to get 33.

$$y=2x^{2}-16x+33$$

Solve for x (complex solution)

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

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

Solve for x

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

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