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154 lines
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HTML
154 lines
7.4 KiB
HTML
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<title>Standard Form</title>
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<h1 align="center">Standard Form</h1>
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<div class="center80">
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<p>What is "Standard Form"?</p>
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<p align="center" class="larger">that depends on what you are dealing with! </p>
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</div>
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<p>I have gathered some common "Standard Form"s here for you..</p>
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<div class="words">
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<p>Note: Standard Form is <b>not</b> the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.</p>
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</div>
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<h2>Standard Form of a Decimal Number</h2>
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<p>In <b>Britain</b> this is another name for <a href="../numbers/scientific-notation.html">Scientific Notation</a>, where you write down a number this way:</p>
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<p class="center"><img src="../numbers/images/scientific-notation.svg" alt="5326.6 = 5.3266 times 10 to the 3" /><br />
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In this example, 5326.6 is written as <b>5.3266 × 10<sup>3</sup></b>,<br>
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because 5326.6 = 5.3266 × 1000 = 5.3266 × 10<sup>3</sup></p>
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<p>In <b>other countries</b> it means "not in expanded form" (see <a href="../numbers/numbers-compose-decompose.html">Composing and Decomposing Numbers</a>):</p>
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<div class="simple">
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<table border="0" align="center">
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<tr align="center">
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<td width="180" class="large">561</td>
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<td width="180" class="large">500 + 60 + 1</td>
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</tr>
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<tr align="center">
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<td><b>Standard Form</b></td>
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<td><b>Expanded Form</b></td>
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</tr>
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</table>
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</div>
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<h2>Standard Form of an Equation</h2>
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<p>The "Standard Form" of an <a href="equation-formula.html">equation</a> is:</p>
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<p align="center"><i>(some expression)</i> <span class="large">= 0</span></p>
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<p>In other words, "= 0" is on the right, and everything else is on the left.</p>
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<div class="example">
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<h3>Example: Put x<sup>2</sup> = 7 into Standard Form</h3>
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<p>Answer:</p>
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<p align="center"><span class="large">x<sup>2</sup> − 7 = 0</span></p>
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</div>
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<h2>Standard Form of a Polynomial</h2>
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<p>The "Standard Form" for writing down a <a href="polynomials.html">polynomial</a> is to put the terms with the highest <a href="degree-expression.html">degree</a> first (like the "2" in x<sup>2</sup> if there is one variable).</p>
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<div class="example">
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<h3>Example: Put this in Standard Form: </h3>
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<h3 align="center">3<b>x<sup>2</sup></b> − 7 + 4<b>x<sup>3</sup></b> + <b>x<sup>6</sup></b></h3>
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<p>The highest degree is 6, so that goes first, then 3, 2 and then the constant last:</p>
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<p align="center" class="large"><b>x<sup>6</sup></b> + 4<b>x<sup>3</sup></b> + 3<b>x<sup>2</sup></b> − 7</p>
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</div>
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<h2>Standard Form of a Linear Equation</h2>
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<p>The "Standard Form" for writing down a <a href="../equation_of_line.html">Linear Equation</a> is</p>
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<p align="center" class="large">Ax + By = C</p>
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<p><b>A</b> shouldn't be negative, <b>A</b> and <b>B</b> shouldn't both be zero, and <b>A</b>, <b>B</b> and <b>C</b> should be integers.</p>
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<div class="example">
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<h3>Example: Put this in Standard Form: </h3>
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<h3 align="center"><b>y = 3x + 2</b></h3>
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<p>Bring 3x to the left: </p>
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<p align="center" class="large">−3x + y = 2</p>
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<p>Multiply all by −1: </p>
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<p align="center" class="large">3x − y = −2</p>
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<p>Note: A = 3, B = −1, C = −2</p>
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</div>
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<p>This form:</p>
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<p align="center" class="large">Ax + By + C = 0</p>
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<p>is sometimes called "Standard Form", but is more properly called the "General Form".</p>
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<h2>Standard Form of a Quadratic Equation</h2>
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<p>The "Standard Form" for writing down a <a href="quadratic-equation.html">Quadratic Equation</a> is </p>
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<p class="center"><img src="images/quadratic-equation.svg" alt="Standard Form of a Quadratic Equation: ax^2 + bx + c = 0" /></p>
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<p align="center">(<b>a</b> not equal to zero)</p>
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<div class="example">
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<h3>Example: Put this in Standard Form: </h3>
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<h3 align="center"><b>x(x−1) = 3</b></h3>
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<p>Expand "x(x-1)": </p>
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<p align="center" class="large">x<sup>2 </sup>− x = 3</p>
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<p>Bring 3 to left: </p>
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<p align="center" class="large">x<sup>2</sup> − x − 3 = 0</p>
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<p>Note: a = 1, b = −1, c = −3</p>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(2218, 2219, 3184, 2220, 2221, 2222, 2223, 2224, 2225, 7130);</script>
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</div>
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<div class="related"><a href="index.html">Algebra Index</a></div>
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