Algebra Examples

$y = - \sqrt{16 - x^{2}}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = - \sqrt{16 - {(- 2)}^{2}}$

Step 2

Simplify $- \sqrt{16 - {(- 2)}^{2}}$ .

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Step 2.1

Raise $- 2$ to the power of $2$ .

$y = - \sqrt{16 - 1 \cdot 4}$

Step 2.2

Multiply $- 1$ by $4$ .

$y = - \sqrt{16 - 4}$

Step 2.3

Subtract $4$ from $16$ .

$y = - \sqrt{12}$

Step 2.4

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.4.1

Factor $4$ out of $12$ .

$y = - \sqrt{4 (3)}$

Step 2.4.2

Rewrite $4$ as $2^{2}$ .

$y = - \sqrt{2^{2} \cdot 3}$

Step 2.5

Pull terms out from under the radical.

$y = - (2 \sqrt{3})$

Step 2.6

Multiply $2$ by $- 1$ .

$y = - 2 \sqrt{3}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = - \sqrt{16 - {(- 1)}^{2}}$

Step 4

Simplify $- \sqrt{16 - {(- 1)}^{2}}$ .

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Step 4.1

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

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Step 4.1.1

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

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Step 4.1.1.1

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

$y = - \sqrt{16 + {(- 1)}^{1} {(- 1)}^{2}}$

Step 4.1.1.2

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

$y = - \sqrt{16 + {(- 1)}^{1 + 2}}$

Step 4.1.2

Add $1$ and $2$ .

$y = - \sqrt{16 + {(- 1)}^{3}}$

Step 4.2

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

$y = - \sqrt{16 - 1}$

Step 4.3

Subtract $1$ from $16$ .

$y = - \sqrt{15}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = - \sqrt{16 - {(0)}^{2}}$

Step 6

Simplify $- \sqrt{16 - {(0)}^{2}}$ .

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Step 6.1

Raising $0$ to any positive power yields $0$ .

$y = - \sqrt{16 - 0}$

Step 6.2

Multiply $- 1$ by $0$ .

$y = - \sqrt{16 + 0}$

Step 6.3

Add $16$ and $0$ .

$y = - \sqrt{16}$

Step 6.4

Rewrite $16$ as $4^{2}$ .

$y = - \sqrt{4^{2}}$

Step 6.5

Pull terms out from under the radical, assuming positive real numbers.

$y = - 1 \cdot 4$

Step 6.6

Multiply $- 1$ by $4$ .

$y = - 4$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = - \sqrt{16 - {(1)}^{2}}$

Step 8

Simplify $- \sqrt{16 - {(1)}^{2}}$ .

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Step 8.1

One to any power is one.

$y = - \sqrt{16 - 1 \cdot 1}$

Step 8.2

Multiply $- 1$ by $1$ .

$y = - \sqrt{16 - 1}$

Step 8.3

Subtract $1$ from $16$ .

$y = - \sqrt{15}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = - \sqrt{16 - {(2)}^{2}}$

Step 10

Simplify $- \sqrt{16 - {(2)}^{2}}$ .

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Step 10.1

Raise $2$ to the power of $2$ .

$y = - \sqrt{16 - 1 \cdot 4}$

Step 10.2

Multiply $- 1$ by $4$ .

$y = - \sqrt{16 - 4}$

Step 10.3

Subtract $4$ from $16$ .

$y = - \sqrt{12}$

Step 10.4

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 10.4.1

Factor $4$ out of $12$ .

$y = - \sqrt{4 (3)}$

Step 10.4.2

Rewrite $4$ as $2^{2}$ .

$y = - \sqrt{2^{2} \cdot 3}$

Step 10.5

Pull terms out from under the radical.

$y = - (2 \sqrt{3})$

Step 10.6

Multiply $2$ by $- 1$ .

$y = - 2 \sqrt{3}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - 2 \sqrt{3} \\ - 1 & - \sqrt{15} \\ 0 & - 4 \\ 1 & - \sqrt{15} \\ 2 & - 2 \sqrt{3} \end{array}$

Step 12