Solve y=-6(x-5)^2+12

$$y = - 6 ( x - 5 ) ^ { 2 } + 12$$

Solve for y

$$y=-6\left(x-5\right)^{2}+12$$

Solution Steps

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

$$y=-6\left(x^{2}-10x+25\right)+12$$

Use the distributive property to multiply -6 by x^{2}-10x+25.

$$y=-6x^{2}+60x-150+12$$

Add -150 and 12 to get -138.

$$y=-6x^{2}+60x-138$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{72-6y}}{6}+5$$

$$x=\frac{\sqrt{72-6y}}{6}+5$$

Solve for x

$$x=-\frac{\sqrt{72-6y}}{6}+5$$

$$x=\frac{\sqrt{72-6y}}{6}+5\text{, }y\leq 12$$