Precalculus Examples

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

Step 1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - {(- 1)}^{2} - 4 \cdot - 1$

Step 2

Simplify $- {(- 1)}^{2} - 4 \cdot - 1$ .

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Step 2.1

Remove parentheses.

$- {(- 1)}^{2} - 4 \cdot - 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 2.2.1.1

Multiply $- 1$ by ${(- 1)}^{2}$ .

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Step 2.2.1.1.1

Raise $- 1$ to the power of $1$ .

${(- 1)}^{1} {(- 1)}^{2} - 4 \cdot - 1$

Step 2.2.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(- 1)}^{1 + 2} - 4 \cdot - 1$

Step 2.2.1.2

Add $1$ and $2$ .

${(- 1)}^{3} - 4 \cdot - 1$

Step 2.2.2

Raise $- 1$ to the power of $3$ .

$- 1 - 4 \cdot - 1$

Step 2.2.3

Multiply $- 4$ by $- 1$ .

$- 1 + 4$

Step 2.3

Add $- 1$ and $4$ .

$3$