Precalculus Examples

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

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

Subtract $2 x^{2}$ from both sides of the equation.

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

Step 1.2.2

Subtract $4$ from both sides of the equation.

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

Step 1.3

Divide each term in $- y = 4 x - 2 x^{2} - 4$ by $- 1$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $- y = 4 x - 2 x^{2} - 4$ by $- 1$ .

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

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Dividing two negative values results in a positive value.

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

Step 1.3.2.2

Divide $y$ by $1$ .

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

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Simplify each term.

Tap for more steps...

Step 1.3.3.1.1

Move the negative one from the denominator of $\frac{4 x}{- 1}$ .

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

Step 1.3.3.1.2

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

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

Step 1.3.3.1.3

Multiply $4$ by $- 1$ .

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

Step 1.3.3.1.4

Move the negative one from the denominator of $\frac{- 2 x^{2}}{- 1}$ .

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

Step 1.3.3.1.5

Rewrite $- 1 \cdot (- 2 x^{2})$ as $- (- 2 x^{2})$ .

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

Step 1.3.3.1.6

Multiply $- 2$ by $- 1$ .

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

Step 1.3.3.1.7

Divide $- 4$ by $- 1$ .

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

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

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

Step 3

Reorder $- 4 x$ and $2 x^{2}$ .

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

Step 4