Fourier half range cosine series: f(t)=-1+4t+t^2, 0<t<=3

[Jpowell]

The function f(t) is defined as followsf(t)=−1+4t+t2,0<t≤3 . Define ^f(t) , an even periodic extension of f(t) and hence select the name of the appropriate Fourier half-range series representation of f^(t).

Enter the following values in the boxes below:​

• 
  [*]
  p​

  =​

  ^​

  f​

  (​

  −​

  1​

  )​

  p=f^(−1)​
  ,
  [*]
  q​

  =​

  ^​

  f​

  (​

  4​

  )​

  q=f^(4)​
  ,
• T​

  T​
  , the period of
  ^​

  f​

  (​

  t​

  )​

  f^(t)​
  .
• I know that the period of the series is 6 and I have tried to work out the series but Im unsure if Im correct and do not know how to apply the values of t given at the end.
• All help will be hugely appreciated