Whakaoti i te y=1/2(x+3)^2+5

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

Whakaoti mō y

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

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+3\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te x^{2}+6x+9.

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

Tāpirihia te \frac{9}{2} ki te 5, ka \frac{19}{2}.

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

Whakaoti mō x (complex solution)

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

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

Whakaoti mō x

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

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