Solve for y
y=\frac{\left(x-2\right)^{2}+4}{2}
Solve for x (complex solution)
x=-\sqrt{2y-4}+2
x=\sqrt{2y-4}+2
Solve for x
x=-\sqrt{2y-4}+2
x=\sqrt{2y-4}+2\text{, }y\geq 2
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y=\frac{1}{2}\left(x^{2}-4x+4\right)+2
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
y=\frac{1}{2}x^{2}-2x+2+2
Use the distributive property to multiply \frac{1}{2} by x^{2}-4x+4.
y=\frac{1}{2}x^{2}-2x+4
Add 2 and 2 to get 4.
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