Find the Standard Form of the Parabola 4x+y^2+2y=-5

$4 x + y^{2} + 2 y = - 5$

Step 1

Subtract $4 x$ from both sides of the equation.

$y^{2} + 2 y = - 5 - 4 x$

Step 2

Complete the square.

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

$a = 1$

$b = 2$

$c = 0 = - 5 - 4 x$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e = - 5 - 4 x$

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$d = 1$

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

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = 0 - \frac{2^{2}}{4 \cdot 1}$

Simplify the right side.

Simplify each term.

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

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

Multiply $4$ by $1$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$e = 0 - 1 \cdot 1$

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

${(y + 1)}^{2} - 1 = - 5 - 4 x$

Step 3

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

Add $1$ to both sides of the equation.

${(y + 1)}^{2} = - 5 - 4 x + 1$

Add $- 5$ and $1$ .

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

Step 4

Factor.

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

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

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

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $4 (- x) + 4 (- 1)$ .

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

Factor $- 1$ out of $- x$ .

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

Rewrite $- 1$ as $- 1 (1)$ .

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

Factor $- 1$ out of $- (x) - 1 (1)$ .

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

Multiply $- 1$ by $4$ .

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

Find the Standard Form of the Parabola 4x+y^2+2y=-5

Related Questions

Support LCMGCF.com by disabling your adblocker.