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

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

Solve for y

$$y=-\left(x-4\right)\left(x-2\right)$$

Solution Steps

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

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

To find the opposite of x^{2}-6x+9, find the opposite of each term.

$$y=-x^{2}+6x-9+1$$

Add -9 and 1 to get -8.

$$y=-x^{2}+6x-8$$

Solve for x (complex solution)

$$x=-\sqrt{1-y}+3$$

$$x=\sqrt{1-y}+3$$

Solve for x

$$x=-\sqrt{1-y}+3$$

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