Solve y=-0.2(x-30)^2+12

$$y = - 0.2 ( x - 30 ) ^ { 2 } + 12$$

Solve for y

$$y=-\frac{\left(x-30\right)^{2}}{5}+12$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-30\right)^{2}.

$$y=-0.2\left(x^{2}-60x+900\right)+12$$

Use the distributive property to multiply -0.2 by x^{2}-60x+900.

$$y=-0.2x^{2}+12x-180+12$$

Add -180 and 12 to get -168.

$$y=-0.2x^{2}+12x-168$$

Solve for x (complex solution)

$$x=-\sqrt{60-5y}+30$$

$$x=\sqrt{60-5y}+30$$

Solve for x

$$x=-\sqrt{60-5y}+30$$

$$x=\sqrt{60-5y}+30\text{, }y\leq 12$$