Resolver y-1=2-(x-1)^2

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

Resolver y

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

Pasos da solución

Usar teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(x-1\right)^{2}.

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

Para calcular o oposto de x^{2}-2x+1, calcula o oposto de cada termo.

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

Resta 1 de 2 para obter 1.

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

Engadir 1 en ambos lados.

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

Suma 1 e 1 para obter 2.

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

Resolver x (complex solution)

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

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

Resolver x

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

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