Solve for y
y=-\frac{\left(x-1\right)^{2}}{2}+3
Solve for x (complex solution)
x=-\sqrt{6-2y}+1
x=\sqrt{6-2y}+1
Solve for x
x=-\sqrt{6-2y}+1
x=\sqrt{6-2y}+1\text{, }y\leq 3
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y=3-\frac{1}{2}\left(x^{2}-2x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
y=3-\frac{1}{2}x^{2}+x-\frac{1}{2}
Use the distributive property to multiply -\frac{1}{2} by x^{2}-2x+1.
y=\frac{5}{2}-\frac{1}{2}x^{2}+x
Subtract \frac{1}{2} from 3 to get \frac{5}{2}.
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