Solve y=(x-1.5)^2-1

$$y = ( x - 1.5 ) ^ { 2 } - 1$$

Solve for y

$$y=\left(x-2.5\right)\left(x-0.5\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1.5\right)^{2}.

$$y=x^{2}-3x+2.25-1$$

Subtract 1 from 2.25 to get 1.25.

$$y=x^{2}-3x+1.25$$

Solve for x (complex solution)

$$x=-\sqrt{y+1}+1.5$$

$$x=\sqrt{y+1}+1.5$$

Solve for x

$$x=-\sqrt{y+1}+1.5$$

$$x=\sqrt{y+1}+1.5\text{, }y\geq -1$$