Solve y=left(x-100right)^2+100

$$y= { \left(x-100 \right) }^{ 2 } +100$$

Solve for y

$$y=\left(x-100\right)^{2}+100$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-100\right)^{2}.

$$y=x^{2}-200x+10000+100$$

Add 10000 and 100 to get 10100.

$$y=x^{2}-200x+10100$$

Solve for x (complex solution)

$$x=-\sqrt{y-100}+100$$

$$x=\sqrt{y-100}+100$$

Solve for x

$$x=-\sqrt{y-100}+100$$

$$x=\sqrt{y-100}+100\text{, }y\geq 100$$