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

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

Solve for y

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

Solution Steps

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

$$y=x^{2}+8x+16-2$$

Subtract 2 from 16 to get 14.

$$y=x^{2}+8x+14$$

Solve for x (complex solution)

$$x=-\left(\sqrt{y+2}+4\right)$$

$$x=\sqrt{y+2}-4$$

Solve for x

$$x=-\left(\sqrt{y+2}+4\right)$$

$$x=\sqrt{y+2}-4\text{, }y\geq -2$$