Solve y=-(x-6)^2-1

$$y = - ( x - 6 ) ^ { 2 } - 1$$

Solve for y

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$y=-\left(x^{2}-12x+36\right)-1$$

To find the opposite of x^{2}-12x+36, find the opposite of each term.

$$y=-x^{2}+12x-36-1$$

Subtract 1 from -36 to get -37.

$$y=-x^{2}+12x-37$$

Solve for x (complex solution)

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

$$x=i\sqrt{y+1}+6$$

Solve for x

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

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