Solve y=mx^2+2

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

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}+2=y$$

Subtract 2 from both sides.

$$mx^{2}=y-2$$

The equation is in standard form.

$$x^{2}m=y-2$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{y-2}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{y-2}{x^{2}}$$

Solve for m

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mx^{2}+2=y$$

Subtract 2 from both sides.

$$mx^{2}=y-2$$

The equation is in standard form.

$$x^{2}m=y-2$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{y-2}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{y-2}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-m^{-\frac{1}{2}}\sqrt{y-2}\text{; }x=m^{-\frac{1}{2}}\sqrt{y-2}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&y=2\text{ and }m=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y-2}{m}}\text{; }x=-\sqrt{\frac{y-2}{m}}\text{, }&\left(y\geq 2\text{ and }m>0\right)\text{ or }\left(y\leq 2\text{ and }m<0\right)\\x\in \mathrm{R}\text{, }&y=2\text{ and }m=0\end{matrix}\right.$$