methods / functions.md.htmlon commit start prelim notes (546a68f)
   1<!DOCTYPE html>
   2<html>
   3  <head>
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   5      <title>functions</title>
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 548</style>
 549  </head>
 550  <body class='markdown-preview'><h1>Linear and Quadratic Functions</h1>
 551<h2>General binomial expansion</h2>
 552<span class="math"><script type="math/tex; mode=display">(a+b)(c+d) = a(c+d) + b(c+d)
 553</script></span>
 554<span class="math"><script type="math/tex; mode=display">= ac+ad+bc+bd
 555</script></span>
 556<h2>Perfect square expansion</h2>
 557<span class="math"><script type="math/tex; mode=display">(a+b)^2=a^2+2ab+b^2
 558</script></span>
 559<h2>Difference of perfect squares</h2>
 560<span class="math"><script type="math/tex; mode=display">a^2-b^2=(a+b)(a-b)
 561</script></span>
 562<h2>Factorising monic quadratics</h2>
 563<span class="math"><script type="math/tex; mode=display">x^2+bx+c = (x+e)(x-f)
 564</script></span>
 565<p>where<br>
 566<span class="math"><script type="math/tex">e \times f = c</script></span><br>
 567<span class="math"><script type="math/tex">e+f = b</script></span></p>
 568<h2>Factorising general quadratics</h2>
 569<span class="math"><script type="math/tex; mode=display">ax^2+bx+c=(x+e)(x+f)
 570</script></span>
 571<p>where<br>
 572<span class="math"><script type="math/tex">e \times f = a \times c</script></span><br>
 573<span class="math"><script type="math/tex">e+f = b</script></span></p>
 574<h2>Completing the square</h2>
 575<span class="math"><script type="math/tex; mode=display">ax^2+bx+c=a(x+{b \over 2a})^2+(c-{b^2 \over 2a})^2
 576</script></span>
 577<h2>Axis of symmetry</h2>
 578<span class="math"><script type="math/tex; mode=display">{vert}_x={-b \over 2a}
 579</script></span>
 580<span class="math"><script type="math/tex; mode=display">x={-b \over 2a}
 581</script></span>
 582<p>(corresponding line)</p></body>
 583</html>