Find the Standard Form of the Parabola x=1/2y^2+4y

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

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Complete the square.

Combine $\frac{1}{2}$ and $y^{2}$ .

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

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

$a = \frac{1}{2}$

$b = 4$

$c = 0 = x$

Consider the vertex form of a parabola.

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

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

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

$d = \frac{4}{2 (\frac{1}{2})}$

Simplify the right side.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator by the reciprocal of the denominator.

$d = 2 \cdot 2$

Multiply $2$ by $2$ .

$d = 4$

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 $e = c - \frac{b^{2}}{4 a}$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $4^{2}$ and $4$ .

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

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator by the reciprocal of the denominator.

$e = 0 - (4 \cdot 2)$

Multiply $4$ by $2$ .

$e = 0 - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$e = 0 - 8$

Subtract $8$ from $0$ .

$e = - 8$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $\frac{1}{2} {(y + 4)}^{2} - 8$ .

$\frac{1}{2} \cdot {(y + 4)}^{2} - 8 = x$

Add $8$ to both sides of the equation.

$\frac{1}{2} \cdot {(y + 4)}^{2} = x + 8$

Multiply each term in $\frac{1}{2} \cdot {(y + 4)}^{2} = x + 8$ by $2$ to eliminate the fractions.

Multiply each term in $\frac{1}{2} \cdot {(y + 4)}^{2} = x + 8$ by $2$ .

$\frac{1}{2} \cdot {(y + 4)}^{2} \cdot 2 = x \cdot 2 + 8 \cdot 2$

Simplify the left side.

Combine $\frac{1}{2}$ and ${(y + 4)}^{2}$ .

$\frac{{(y + 4)}^{2}}{2} \cdot 2 = x \cdot 2 + 8 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{{(y + 4)}^{2}}{2} \cdot 2 = x \cdot 2 + 8 \cdot 2$

Rewrite the expression.

${(y + 4)}^{2} = x \cdot 2 + 8 \cdot 2$

Simplify the right side.

Simplify each term.

Move $2$ to the left of $x$ .

${(y + 4)}^{2} = 2 \cdot x + 8 \cdot 2$

Multiply $8$ by $2$ .

${(y + 4)}^{2} = 2 x + 16$

Factor $2$ out of $2 x + 16$ .

Factor $2$ out of $2 x$ .

${(y + 4)}^{2} = 2 (x) + 16$

Factor $2$ out of $16$ .

${(y + 4)}^{2} = 2 x + 2 \cdot 8$

Factor $2$ out of $2 x + 2 \cdot 8$ .

${(y + 4)}^{2} = 2 (x + 8)$

Find the Standard Form of the Parabola x=1/2y^2+4y

Related Questions

Support LCMGCF.com by disabling your adblocker.