Solve y=a+bx^2

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

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract a from both sides.

$$bx^{2}=y-a$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for b

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

Steps for Solving Linear Equation

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

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

Subtract a from both sides.

$$bx^{2}=y-a$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for a

$$a=y-bx^{2}$$