Write as a Function of x 5x^2+4y=(y+1)/4

$5 x^{2} + 4 y = \frac{y + 1}{4}$

Step 1

Multiply both sides by $4$ .

$(5 x^{2} + 4 y) \cdot 4 = \frac{y + 1}{4} \cdot 4$

Step 2

Simplify.

Simplify the left side.

Simplify $(5 x^{2} + 4 y) \cdot 4$ .

Apply the distributive property.

$5 x^{2} \cdot 4 + 4 y \cdot 4 = \frac{y + 1}{4} \cdot 4$

Multiply.

Multiply $4$ by $5$ .

$20 x^{2} + 4 y \cdot 4 = \frac{y + 1}{4} \cdot 4$

Multiply $4$ by $4$ .

$20 x^{2} + 16 y = \frac{y + 1}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$20 x^{2} + 16 y = \frac{y + 1}{4} \cdot 4$

Rewrite the expression.

$20 x^{2} + 16 y = y + 1$

Step 3

Solve for $y$ .

Move all terms containing $y$ to the left side of the equation.

Subtract $y$ from both sides of the equation.

$20 x^{2} + 16 y - y = 1$

Subtract $y$ from $16 y$ .

$20 x^{2} + 15 y = 1$

Subtract $20 x^{2}$ from both sides of the equation.

$15 y = 1 - 20 x^{2}$

Divide each term in $15 y = 1 - 20 x^{2}$ by $15$ and simplify.

Divide each term in $15 y = 1 - 20 x^{2}$ by $15$ .

$\frac{15 y}{15} = \frac{1}{15} + \frac{- 20 x^{2}}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{1}{15} + \frac{- 20 x^{2}}{15}$

Divide $y$ by $1$ .

$y = \frac{1}{15} + \frac{- 20 x^{2}}{15}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 20$ and $15$ .

Factor $5$ out of $- 20 x^{2}$ .

$y = \frac{1}{15} + \frac{5 (- 4 x^{2})}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

$y = \frac{1}{15} + \frac{5 (- 4 x^{2})}{5 (3)}$

Cancel the common factor.

$y = \frac{1}{15} + \frac{5 (- 4 x^{2})}{5 \cdot 3}$

Rewrite the expression.

$y = \frac{1}{15} + \frac{- 4 x^{2}}{3}$

Move the negative in front of the fraction.

$y = \frac{1}{15} - \frac{4 x^{2}}{3}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{1}{15} - \frac{4 x^{2}}{3}$

Write as a Function of x 5x^2+4y=(y+1)/4

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