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

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

Solve for y

$$y=-\left(x-3\right)\left(x+1\right)$$

Solution Steps

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

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

To find the opposite of x^{2}-2x+1, find the opposite of each term.

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

Subtract 1 from 4 to get 3.

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

Solve for x (complex solution)

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

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

Solve for x

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

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