Algebra Examples

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

Step 1

Write $f (x) = - {(x + 1)}^{2} + 4$ as an equation.

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

Step 2

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

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

Step 3

Subtract $4$ from both sides of the equation.

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

Step 4

Divide each term in $- {(x + 1)}^{2} = y - 4$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- {(x + 1)}^{2} = y - 4$ by $- 1$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2

Divide ${(x + 1)}^{2}$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative one from the denominator of $\frac{y}{- 1}$ .

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

Step 4.3.1.2

Rewrite $- 1 \cdot y$ as $- y$ .

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

Step 4.3.1.3

Divide $- 4$ by $- 1$ .

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

Step 5

Factor.

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Step 5.1

Factor $- 1$ out of $- y$ .

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

Step 5.2

Rewrite $4$ as $- 1 (- 4)$ .

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

Step 5.3

Factor $- 1$ out of $- (y) - 1 (- 4)$ .

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