Solve y=-1/2(x-1)^2+3

$$y = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 3$$

Solve for y

$$y=-\frac{\left(x-1\right)^{2}}{2}+3$$

Solution Steps

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

$$y=-\frac{1}{2}\left(x^{2}-2x+1\right)+3$$

Use the distributive property to multiply -\frac{1}{2} by x^{2}-2x+1.

$$y=-\frac{1}{2}x^{2}+x-\frac{1}{2}+3$$

Add -\frac{1}{2} and 3 to get \frac{5}{2}.

$$y=-\frac{1}{2}x^{2}+x+\frac{5}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{6-2y}+1$$

$$x=\sqrt{6-2y}+1$$

Solve for x

$$x=-\sqrt{6-2y}+1$$

$$x=\sqrt{6-2y}+1\text{, }y\leq 3$$