Whakaoti i te (x-1)^2=-y+10/3

$$( x - 1 ) ^ { 2 } = - y + \frac { 10 } { 3 }$$

Whakaoti mō y

$$y=-\left(x-1\right)^{2}+\frac{10}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$x^{2}-2x+1=-y+\frac{10}{3}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-y+\frac{10}{3}=x^{2}-2x+1$$

Tangohia te \frac{10}{3} mai i ngā taha e rua.

$$-y=x^{2}-2x+1-\frac{10}{3}$$

Tangohia te \frac{10}{3} i te 1, ka -\frac{7}{3}.

$$-y=x^{2}-2x-\frac{7}{3}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y}{-1}=\frac{x^{2}-2x-\frac{7}{3}}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$y=\frac{x^{2}-2x-\frac{7}{3}}{-1}$$

Whakawehe x^{2}-2x-\frac{7}{3} ki te -1.

$$y=\frac{7}{3}+2x-x^{2}$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

$$x=\frac{\sqrt{30-9y}}{3}+1$$

Whakaoti mō x

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

$$x=\frac{\sqrt{30-9y}}{3}+1\text{, }y\leq \frac{10}{3}$$