Algebra Examples

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

Step 1

Simplify $x \sqrt{16 - x^{2}}$ .

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Step 1.1

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

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

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x$ .

$y = x \sqrt{(4 + x) (4 - x)}$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(- 2 \sqrt{2}, 2 \sqrt{2})$

Decreasing on: $(- 4, - 2 \sqrt{2}), (2 \sqrt{2}, 4)$

Step 3