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

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

y uchun yechish

$$y=\frac{\left(x+3\right)^{2}+10}{2}$$

Yechim qadamlari

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

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

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

$$y=\frac{1}{2}x^{2}+3x+\frac{9}{2}+5$$

\frac{19}{2} olish uchun \frac{9}{2} va 5'ni qo'shing.

$$y=\frac{1}{2}x^{2}+3x+\frac{19}{2}$$

x uchun yechish (complex solution)

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

$$x=\sqrt{2\left(y-5\right)}-3$$

x uchun yechish

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

$$x=\sqrt{2\left(y-5\right)}-3\text{, }y\geq 5$$