Find the Vertex Form x^2+y^2+2x-2y-14=0

$x^{2} + y^{2} + 2 x - 2 y - 14 = 0$

Add $14$ to both sides of the equation.

$x^{2} + y^{2} + 2 x - 2 y = 14$

Complete the square for $x^{2} + 2 x$ .

Tap for more steps…

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = 2, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{2}{2 (1)}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$d = \frac{2}{2 \cdot 1}$

Divide $1$ by $1$ .

$d = 1$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps…

Simplify each term.

Tap for more steps…

Raise $2$ to the power of $2$ .

$e = 0 - \frac{4}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 0 - \frac{4}{4}$

Divide $4$ by $4$ .

$e = 0 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$e = 0 - 1$

Subtract $1$ from $0$ .

$e = - 1$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(x + 1)}^{2} - 1$

Substitute ${(x + 1)}^{2} - 1$ for $x^{2} + 2 x$ in the equation $x^{2} + y^{2} + 2 x - 2 y = 14$ .

${(x + 1)}^{2} - 1 + y^{2} - 2 y = 14$

Move $- 1$ to the right side of the equation by adding $1$ to both sides.

${(x + 1)}^{2} + y^{2} - 2 y = 14 + 1$

Complete the square for $y^{2} - 2 y$ .

Tap for more steps…

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = - 2, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = - \frac{2}{2 (1)}$

Simplify the right side.

Tap for more steps…

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$d = - \frac{2}{2 \cdot 1}$

Divide $1$ by $1$ .

$d = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$d = - 1$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps…

Simplify each term.

Tap for more steps…

Raise $- 2$ to the power of $2$ .

$e = 0 - \frac{4}{4 \cdot 1}$

Multiply $4$ by $1$ .

$e = 0 - \frac{4}{4}$

Divide $4$ by $4$ .

$e = 0 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$e = 0 - 1$

Subtract $1$ from $0$ .

$e = - 1$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(y - 1)}^{2} - 1$

Substitute ${(y - 1)}^{2} - 1$ for $y^{2} - 2 y$ in the equation $x^{2} + y^{2} + 2 x - 2 y = 14$ .

${(x + 1)}^{2} + {(y - 1)}^{2} - 1 = 14 + 1$

Move $- 1$ to the right side of the equation by adding $1$ to both sides.

${(x + 1)}^{2} + {(y - 1)}^{2} = 14 + 1 + 1$

Simplify $14 + 1 + 1$ .

Tap for more steps…

Add $14$ and $1$ .

${(x + 1)}^{2} + {(y - 1)}^{2} = 15 + 1$

Add $15$ and $1$ .

${(x + 1)}^{2} + {(y - 1)}^{2} = 16$

Find the Vertex Form x^2+y^2+2x-2y-14=0

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store