Solve y=-(x-5)^2-3

$$y = - ( x - 5 ) ^ { 2 } - 3$$

Solve for y

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$y=-\left(x^{2}-10x+25\right)-3$$

To find the opposite of x^{2}-10x+25, find the opposite of each term.

$$y=-x^{2}+10x-25-3$$

Subtract 3 from -25 to get -28.

$$y=-x^{2}+10x-28$$

Solve for x (complex solution)

$$x=-i\sqrt{y+3}+5$$

$$x=i\sqrt{y+3}+5$$

Solve for x

$$x=-\sqrt{-y-3}+5$$

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