Solve y=-3(x+8)^2+108(4)

$$y = - 3 ( x + 8 ) ^ { 2 } + 108 ( 4 )$$

Solve for y

$$y=3\left(4-x\right)\left(x+20\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$y=-3\left(x^{2}+16x+64\right)+108\times 4$$

Use the distributive property to multiply -3 by x^{2}+16x+64.

$$y=-3x^{2}-48x-192+108\times 4$$

Multiply 108 and 4 to get 432.

$$y=-3x^{2}-48x-192+432$$

Add -192 and 432 to get 240.

$$y=-3x^{2}-48x+240$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{1296-3y}}{3}-8$$

$$x=\frac{\sqrt{1296-3y}}{3}-8$$

Solve for x

$$x=-\frac{\sqrt{1296-3y}}{3}-8$$

$$x=\frac{\sqrt{1296-3y}}{3}-8\text{, }y\leq 432$$