Precalculus Examples

$4 x^{2} - 16 x + 16 y + 32 = 0$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $4 x^{2}$ from both sides of the equation.

$- 16 x + 16 y + 32 = - 4 x^{2}$

Step 1.1.2

Add $16 x$ to both sides of the equation.

$16 y + 32 = - 4 x^{2} + 16 x$

Step 1.1.3

Subtract $32$ from both sides of the equation.

$16 y = - 4 x^{2} + 16 x - 32$

Step 1.2

Divide each term in $16 y = - 4 x^{2} + 16 x - 32$ by $16$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $16 y = - 4 x^{2} + 16 x - 32$ by $16$ .

$\frac{16 y}{16} = \frac{- 4 x^{2}}{16} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $16$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{16 y}{16} = \frac{- 4 x^{2}}{16} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 x^{2}}{16} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Cancel the common factor of $- 4$ and $16$ .

Tap for more steps...

Step 1.2.3.1.1.1

Factor $4$ out of $- 4 x^{2}$ .

$y = \frac{4 (- x^{2})}{16} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.1.2.1

Factor $4$ out of $16$ .

$y = \frac{4 (- x^{2})}{4 (4)} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{4 (- x^{2})}{4 \cdot 4} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- x^{2}}{4} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{4} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.3

Cancel the common factor of $16$ .

Tap for more steps...

Step 1.2.3.1.3.1

Cancel the common factor.

$y = - \frac{x^{2}}{4} + \frac{16 x}{16} + \frac{- 32}{16}$

Step 1.2.3.1.3.2

Divide $x$ by $1$ .

$y = - \frac{x^{2}}{4} + x + \frac{- 32}{16}$

Step 1.2.3.1.4

Divide $- 32$ by $16$ .

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

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 terms.

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

Step 4

Remove parentheses.

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

Step 5