y=1/5(x-3)^2+5 eching

$$y = \frac { 1 } { 5 } ( x - 3 ) ^ { 2 } + 5$$

y uchun yechish

$$y=\frac{\left(x-3\right)^{2}+25}{5}$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$y=\frac{1}{5}\left(x^{2}-6x+9\right)+5$$

\frac{1}{5} ga x^{2}-6x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=\frac{1}{5}x^{2}-\frac{6}{5}x+\frac{9}{5}+5$$

\frac{34}{5} olish uchun \frac{9}{5} va 5'ni qo'shing.

$$y=\frac{1}{5}x^{2}-\frac{6}{5}x+\frac{34}{5}$$

x uchun yechish (complex solution)

$$x=-\sqrt{5\left(y-5\right)}+3$$

$$x=\sqrt{5\left(y-5\right)}+3$$

x uchun yechish

$$x=-\sqrt{5\left(y-5\right)}+3$$

$$x=\sqrt{5\left(y-5\right)}+3\text{, }y\geq 5$$