Solve y=-1(x-10)^2+13

$$y = - 1 ( x - 10 ) ^ { 2 } + 13$$

Solve for y

$$y=-\left(x-10\right)^{2}+13$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$y=-\left(x^{2}-20x+100\right)+13$$

To find the opposite of x^{2}-20x+100, find the opposite of each term.

$$y=-x^{2}+20x-100+13$$

Add -100 and 13 to get -87.

$$y=-x^{2}+20x-87$$

Solve for x (complex solution)

$$x=-\sqrt{13-y}+10$$

$$x=\sqrt{13-y}+10$$

Solve for x

$$x=-\sqrt{13-y}+10$$

$$x=\sqrt{13-y}+10\text{, }y\leq 13$$