Solve y=-1/2(x-3)^2+5

$$y = - \frac { 1 } { 2 } ( x - 3 ) ^ { 2 } + 5$$

Solve for y

$$y=-\frac{\left(x-3\right)^{2}}{2}+5$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$y=-\frac{1}{2}\left(x^{2}-6x+9\right)+5$$

Use the distributive property to multiply -\frac{1}{2} by x^{2}-6x+9.

$$y=-\frac{1}{2}x^{2}+3x-\frac{9}{2}+5$$

Add -\frac{9}{2} and 5 to get \frac{1}{2}.

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

Solve for x (complex solution)

$$x=-\sqrt{10-2y}+3$$

$$x=\sqrt{10-2y}+3$$

Solve for x

$$x=-\sqrt{10-2y}+3$$

$$x=\sqrt{10-2y}+3\text{, }y\leq 5$$