title: How to find c1 in Big Theta?
body: <p>In the case that we have polynomial:</p>
  
  <pre><code>f(n) = 8n^2 - 4n + 2
  </code></pre>
  
  <p>We will then have g(n) = n^2</p>
  
  <pre><code>BigTheta(f(n)) = 0 &lt;= c1g(n) &lt;= f(n) &lt;= c2g(n), n &gt; n0
  </code></pre>
  
  <p>I know that to find c2, we would add all coefficients:
  8  -  4  +  2
  And therefore c2 = 2, correct?
  But what about c1?
  Will c1 ALWAYS be equal to 1? Or will it always be equal to the smallest positive coefficient?
  What is the general rule here?</p>
  
  <p>Another example, if we have:</p>
  
  <pre><code>f(n) = 9n^2 + 3n/2 + 1/4
  g(n) =  n^2
  </code></pre>
  
  <p>I know that c2 = 10.75
  But will c1 = 1 or 1/4?</p>
  
  <p>I'm looking for a general rule to figure out c1 giving me a tight bound.</p>
  
  <p>Thank you very much.</p>