Calculus Examples

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

Step 1

Rewrite the equation as $a x^{2} + b x + c = y$ .

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

Step 2

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $b x$ from both sides of the equation.

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

Step 2.2

Subtract $c$ from both sides of the equation.

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

Step 3

Divide each term in $a x^{2} = y - b x - c$ by $x^{2}$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $a x^{2} = y - b x - c$ by $x^{2}$ .

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $x^{2}$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $a$ by $1$ .

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

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $x$ and $x^{2}$ .

Tap for more steps...

Step 3.3.1.1.1

Factor $x$ out of $- b x$ .

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

Step 3.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.1.2.1

Factor $x$ out of $x^{2}$ .

$a = \frac{y}{x^{2}} + \frac{x (- b)}{x \cdot x} + \frac{- c}{x^{2}}$

Step 3.3.1.1.2.2

Cancel the common factor.

$a = \frac{y}{x^{2}} + \frac{x (- b)}{x \cdot x} + \frac{- c}{x^{2}}$

Step 3.3.1.1.2.3

Rewrite the expression.

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

Step 3.3.1.2

Move the negative in front of the fraction.

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

Step 3.3.1.3

Move the negative in front of the fraction.

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