y=2(x-1)^2-3 eching

$$y = 2 ( x - 1 ) ^ { 2 } - 3$$

y uchun yechish

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

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

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

2 ga x^{2}-2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=2x^{2}-4x+2-3$$

-1 olish uchun 2 dan 3 ni ayirish.

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

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{2y+6}}{2}+1$$

$$x=\frac{\sqrt{2y+6}}{2}+1$$

x uchun yechish

$$x=-\frac{\sqrt{2y+6}}{2}+1$$

$$x=\frac{\sqrt{2y+6}}{2}+1\text{, }y\geq -3$$