Whakaoti i te y=ax^2+bx+c

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

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx-y+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=c\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$ax^{2}+bx+c=y$$

Tangohia te bx mai i ngā taha e rua.

$$ax^{2}+c=y-bx$$

Tangohia te c mai i ngā taha e rua.

$$ax^{2}=y-bx-c$$

He hanga arowhānui tō te whārite.

$$x^{2}a=-bx+y-c$$

Whakawehea ngā taha e rua ki te x^{2}.

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

Mā te whakawehe ki te x^{2} ka wetekia te whakareanga ki te x^{2}.

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

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}b=-\frac{ax^{2}-y+c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&y=c\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$ax^{2}+bx+c=y$$

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

$$bx+c=y-ax^{2}$$

Tangohia te c mai i ngā taha e rua.

$$bx=y-ax^{2}-c$$

Whakaraupapatia anō ngā kīanga tau.

$$bx=-ax^{2}+y-c$$

He hanga arowhānui tō te whārite.

$$xb=-ax^{2}+y-c$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xb}{x}=\frac{-ax^{2}+y-c}{x}$$

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

$$b=\frac{-ax^{2}+y-c}{x}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{bx-y+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=c\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$ax^{2}+bx+c=y$$

Tangohia te bx mai i ngā taha e rua.

$$ax^{2}+c=y-bx$$

Tangohia te c mai i ngā taha e rua.

$$ax^{2}=y-bx-c$$

He hanga arowhānui tō te whārite.

$$x^{2}a=-bx+y-c$$

Whakawehea ngā taha e rua ki te x^{2}.

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

Mā te whakawehe ki te x^{2} ka wetekia te whakareanga ki te x^{2}.

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

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{ax^{2}-y+c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&y=c\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$ax^{2}+bx+c=y$$

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

$$bx+c=y-ax^{2}$$

Tangohia te c mai i ngā taha e rua.

$$bx=y-ax^{2}-c$$

Whakaraupapatia anō ngā kīanga tau.

$$bx=-ax^{2}+y-c$$

He hanga arowhānui tō te whārite.

$$xb=-ax^{2}+y-c$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xb}{x}=\frac{-ax^{2}+y-c}{x}$$

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

$$b=\frac{-ax^{2}+y-c}{x}$$