Solve y=-3(x+4)^2-1

$$y = - 3 ( x + 4 ) ^ { 2 } - 1$$

Solve for y

$$y=-3\left(x+4\right)^{2}-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$y=-3\left(x^{2}+8x+16\right)-1$$

Use the distributive property to multiply -3 by x^{2}+8x+16.

$$y=-3x^{2}-24x-48-1$$

Subtract 1 from -48 to get -49.

$$y=-3x^{2}-24x-49$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{-3y-3}}{3}-4$$

$$x=\frac{\sqrt{-3y-3}}{3}-4$$

Solve for x

$$x=-\frac{\sqrt{-3y-3}}{3}-4$$

$$x=\frac{\sqrt{-3y-3}}{3}-4\text{, }y\leq -1$$