Write as a Function of x x^2-6x=2x-4y

$x^{2} - 6 x = 2 x - 4 y$

Step 1

Rewrite the equation as $2 x - 4 y = x^{2} - 6 x$ .

$2 x - 4 y = x^{2} - 6 x$

Step 2

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

Subtract $2 x$ from both sides of the equation.

$- 4 y = x^{2} - 6 x - 2 x$

Subtract $2 x$ from $- 6 x$ .

$- 4 y = x^{2} - 8 x$

Step 3

Divide each term in $- 4 y = x^{2} - 8 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = x^{2} - 8 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{x^{2}}{- 4} + \frac{- 8 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{x^{2}}{- 4} + \frac{- 8 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{x^{2}}{- 4} + \frac{- 8 x}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{4} + \frac{- 8 x}{- 4}$

Cancel the common factor of $- 8$ and $- 4$ .

Factor $- 4$ out of $- 8 x$ .

$y = - \frac{x^{2}}{4} + \frac{- 4 (2 x)}{- 4}$

Cancel the common factors.

Factor $- 4$ out of $- 4$ .

$y = - \frac{x^{2}}{4} + \frac{- 4 (2 x)}{- 4 (1)}$

Cancel the common factor.

$y = - \frac{x^{2}}{4} + \frac{- 4 (2 x)}{- 4 \cdot 1}$

Rewrite the expression.

$y = - \frac{x^{2}}{4} + \frac{2 x}{1}$

Divide $2 x$ by $1$ .

$y = - \frac{x^{2}}{4} + 2 x$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{x^{2}}{4} + 2 x$

Write as a Function of x x^2-6x=2x-4y

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