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I'm facing a problem with Manipulate here, It just plots a blank xy-axis. 

Manipulate[ Plot[FourierTrigSeries[-x^2 + a x, x, 10], {x, -2 Pi, 2 Pi}], {a, -10, 10}]
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    $\begingroup$ You need to add Evaluate[]: Plot[Evaluate[FourierTrigSeries[(* stuff *)], (* stuff *)] $\endgroup$ Commented Oct 1, 2018 at 19:18
  • $\begingroup$ i didn't understand, what does evaluate do in this case? $\endgroup$ Commented Oct 1, 2018 at 19:23

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J.M.'s advice, given in his comment, is one solution. Here is another using the plot option Evaluated. I also add custom x-axis ticks and give the option Appearance -> "Labeled" to the control variable a to make the manipulation more user friendly.

Manipulate[ Plot[FourierTrigSeries[-x^2 + a x, x, 10], {x, -2 Pi, 2 Pi}, Ticks -> {Subdivide[-2 Pi, 2 Pi, 8], Automatic}, Evaluated -> True], {a, -10, 10, .2, Appearance -> "Labeled"}]

demo

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