Algebra Examples

$x = \sqrt{1 - y^{2}}$

Step 1

Simplify $\sqrt{1 - y^{2}}$ .

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$x = \sqrt{1^{2} - y^{2}}$

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 $a = 1$ and $b = y$ .

$x = \sqrt{(1 + y) (1 - y)}$

Step 2

The domain in terms of $y$ are all the $y$ values that make the radicand non-negative.

$[- 1, 1]$

${y | - 1 \leq y \leq 1}$

Step 3

The final answer is .

Step 4

The end points are $(, S E T, x | - 1), (, 1)$ .

$(, S E T, x | - 1), (, 1)$

Step 5

The square root can be graphed using the points around the vertex $(, S E T, x | - 1), (, 1),$

$\begin{array}{c} x & y \\ S E \end{array}$

Step 6