Whakaoti i te y=x^2+ax+a

$$y = x ^ { 2 } + a x + a$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&y=1\text{ and }x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}+ax+a=y$$

Tangohia te x^{2} mai i ngā taha e rua.

$$ax+a=y-x^{2}$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

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

Whakawehea ngā taha e rua ki te x+1.

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

Mā te whakawehe ki te x+1 ka wetekia te whakareanga ki te x+1.

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

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{x^{2}-y}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&y=1\text{ and }x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x^{2}+ax+a=y$$

Tangohia te x^{2} mai i ngā taha e rua.

$$ax+a=y-x^{2}$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

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

Whakawehea ngā taha e rua ki te x+1.

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

Mā te whakawehe ki te x+1 ka wetekia te whakareanga ki te x+1.

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

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{4y+a^{2}-4a}-a}{2}$$

$$x=\frac{-\sqrt{4y+a^{2}-4a}-a}{2}$$

Whakaoti mō x

$$x=\frac{\sqrt{4y+a^{2}-4a}-a}{2}$$

$$x=\frac{-\sqrt{4y+a^{2}-4a}-a}{2}\text{, }y\geq -\frac{a^{2}}{4}+a$$