Solve -(left(-1+xright)^2)+1=y

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

Solve for y

$$y=x\left(2-x\right)$$

Solution Steps

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

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

To find the opposite of 1-2x+x^{2}, find the opposite of each term.

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

Add -1 and 1 to get 0.

$$2x-x^{2}=y$$

Swap sides so that all variable terms are on the left hand side.

$$y=2x-x^{2}$$

Solve for x (complex solution)

$$x=-\sqrt{1-y}+1$$

$$x=\sqrt{1-y}+1$$

Solve for x

$$x=-\sqrt{1-y}+1$$

$$x=\sqrt{1-y}+1\text{, }y\leq 1$$