Precalculus Examples

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

Step 1

Write $f (x) = - 4 {(x + 2)}^{2} + 5$ as an equation.

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

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.

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

Step 3

Subtract $5$ from both sides of the equation.

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

Step 4

Divide each term in $- 4 {(x + 2)}^{2} = y - 5$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 {(x + 2)}^{2} = y - 5$ by $- 4$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

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

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

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 in front of the fraction.

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

Step 4.3.1.2

Dividing two negative values results in a positive value.

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

Step 5

Factor.

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Step 5.1

Combine the numerators over the common denominator.

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

Step 5.2

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

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

Step 5.3

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 5.4

Factor $- 1$ out of $- (y) - 1 (- 5)$ .

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

Step 5.5

Move the negative in front of the fraction.

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

Step 5.6

Reorder terms.

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

Step 5.7

Remove parentheses.

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

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