Solve y+3=-1/16(x+1)^2

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

Solve for y

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

Use the distributive property to multiply -\frac{1}{16} by x^{2}+2x+1.

$$y+3=-\frac{1}{16}x^{2}-\frac{1}{8}x-\frac{1}{16}$$

Subtract 3 from both sides.

$$y=-\frac{1}{16}x^{2}-\frac{1}{8}x-\frac{1}{16}-3$$

Subtract 3 from -\frac{1}{16} to get -\frac{49}{16}.

$$y=-\frac{1}{16}x^{2}-\frac{1}{8}x-\frac{49}{16}$$

Solve for x (complex solution)

$$x=-4\sqrt{-y-3}-1$$

$$x=4\sqrt{-y-3}-1$$

Solve for x

$$x=-4\sqrt{-y-3}-1$$

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