Solve y=-3(x-10)^2+13

$$y = - 3 ( x - 10 ) ^ { 2 } + 13$$

Solve for y

$$y=-3\left(x-10\right)^{2}+13$$

Solution Steps

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

$$y=-3\left(x^{2}-20x+100\right)+13$$

Use the distributive property to multiply -3 by x^{2}-20x+100.

$$y=-3x^{2}+60x-300+13$$

Add -300 and 13 to get -287.

$$y=-3x^{2}+60x-287$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{39-3y}}{3}+10$$

$$x=\frac{\sqrt{39-3y}}{3}+10$$

Solve for x

$$x=-\frac{\sqrt{39-3y}}{3}+10$$

$$x=\frac{\sqrt{39-3y}}{3}+10\text{, }y\leq 13$$