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2<html>
3 <head>
4 <meta charset="utf-8" />
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>