methods / functions2.md.htmlon commit [spec] minor clarifications to calculus section of sac notes (065aae3)
   1<h1>Linear and Quadratic Functions</h1>
   2<h2>General binomial expansion</h2>
   3<span class="math"><script type="math/tex; mode=display">(a+b)(c+d) = a(c+d) + b(c+d)
   4</script></span>
   5<span class="math"><script type="math/tex; mode=display">= ac+ad+bc+bd
   6</script></span>
   7<h2>Perfect square expansion</h2>
   8<span class="math"><script type="math/tex; mode=display">(a+b)^2=a^2+2ab+b^2
   9</script></span>
  10<h2>Difference of perfect squares</h2>
  11<span class="math"><script type="math/tex; mode=display">a^2-b^2=(a+b)(a-b)
  12</script></span>
  13<h2>Factorising monic quadratics</h2>
  14<span class="math"><script type="math/tex; mode=display">x^2+bx+c = (x+e)(x-f)
  15</script></span>
  16<p>where<br>
  17<span class="math"><script type="math/tex">e \times f = c</script></span><br>
  18<span class="math"><script type="math/tex">e+f = b</script></span></p>
  19<h2>Factorising general quadratics</h2>
  20<p><span class="math"><script type="math/tex">ax^2+bx+c=(x+e)(x+f)</script></span></p>
  21<p>where<br>
  22<span class="math"><script type="math/tex">e \times f = a \times c</script></span><br>
  23<span class="math"><script type="math/tex">e+f = b</script></span></p>
  24<h2>Completing the square</h2>
  25<p><span class="math"><script type="math/tex">ax^2+bx+c=a(x + (b \over 2a))^2+(c-{b^2 \over 2a})^2</script></span></p>
  26<h2>Axis of symmetry</h2>
  27<p><span class="math"><script type="math/tex">{vert}_x={-b \over 2a}</script></span></p>
  28<p><span class="math"><script type="math/tex">x={-b \over 2a}</script></span><br>
  29(corresponding line)</p>