Solve y=-3(x+6)^2+5

$$y = - 3 ( x + 6 ) ^ { 2 } + 5$$

Solve for y

$$y=-3\left(x+6\right)^{2}+5$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$y=-3\left(x^{2}+12x+36\right)+5$$

Use the distributive property to multiply -3 by x^{2}+12x+36.

$$y=-3x^{2}-36x-108+5$$

Add -108 and 5 to get -103.

$$y=-3x^{2}-36x-103$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{15-3y}}{3}-6$$

$$x=\frac{\sqrt{15-3y}}{3}-6$$

Solve for x

$$x=-\frac{\sqrt{15-3y}}{3}-6$$

$$x=\frac{\sqrt{15-3y}}{3}-6\text{, }y\leq 5$$