Solve y=(x-1)^2-14

$$y = ( x - 1 ) ^ { 2 } - 14$$

Solve for y

$$y=\left(x-1\right)^{2}-14$$

Solution Steps

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

$$y=x^{2}-2x+1-14$$

Subtract 14 from 1 to get -13.

$$y=x^{2}-2x-13$$

Solve for x (complex solution)

$$x=-\sqrt{y+14}+1$$

$$x=\sqrt{y+14}+1$$

Solve for x

$$x=-\sqrt{y+14}+1$$

$$x=\sqrt{y+14}+1\text{, }y\geq -14$$