 <p>if we have function f(n) = 3n^2-9n , lower order terms and costants can be ignored, we consider higher order terms ,because they play major role in growth of function. By considering only higher order term we can easily find the upper bound, here is the example.</p> <pre><code> f(n)= 3n^2-9n For all sufficient large value of n&gt;=1, 3n^2&lt;=3n^2 and -9n &lt;= n^2 thus, f(n)=3n^2 -9n &lt;= 3n^2 + n^2 &lt;= 4n^2 *The upper bound of f(n) is 4n^2 , that means for all sufficient large value of n&gt;=1, the value of f(n) wouldn't be greater than 4n^2.* therefore, f(n)= Θ(n^2) where c=4 and n0=1 </code></pre> <p><img src="https://i.stack.imgur.com/5vf3g.jpg" alt="enter image description here"></p> <p><strong>we can directly find the upper bound by saying to ignore lower order terms and constants in the equation f(n)= 3n^2-9n , result will be the same Θ(n^2)</strong></p>