Solve y=kx^2+2x+c

$$y = k x ^ { 2 } + 2 x + c$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

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

$$kx^{2}+2x+c=y$$

Subtract 2x from both sides.

$$kx^{2}+c=y-2x$$

Subtract c from both sides.

$$kx^{2}=y-2x-c$$

The equation is in standard form.

$$x^{2}k=-2x+y-c$$

Divide both sides by x^{2}.

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

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

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

Solve for k

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

Steps for Solving Linear Equation

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

$$kx^{2}+2x+c=y$$

Subtract 2x from both sides.

$$kx^{2}+c=y-2x$$

Subtract c from both sides.

$$kx^{2}=y-2x-c$$

The equation is in standard form.

$$x^{2}k=-2x+y-c$$

Divide both sides by x^{2}.

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

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

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

Solve for c

$$c=y-2x-kx^{2}$$