Solve y=ax^2+b+c

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract b from both sides.

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for a

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

Steps for Solving Linear Equation

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

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

Subtract b from both sides.

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

Subtract c from both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for b

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