I'm trying to generate this simple graph using the Manipulate function

f[x_] := a x + b x^2;
Manipulate[Plot[f[x], {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

However, Mathematica doesn't return any graph! If instead of the above, I use now

Manipulate[Plot[a x + b x^2, {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

I can get what I wanted. Any thoughs on why the manipulate doesn't work with functions? Thanks!

  • $\begingroup$ This is covered in the "Possible Issues" section of the documentation for Manipulate. See example after Manipulate only "notices" explicit visible parameters $\endgroup$
    – Bob Hanlon
    Jun 30, 2020 at 2:02

1 Answer 1


The problem is that you must pass a and b to the function. Try f[3] with your current definition and you get 3a + 9b which cannot be plotted. When using SetDelayed (:=), it cannot see that there is an a and b inside the function so it does not know where to assign the values. Instead, try this:

f[x_, a_, b_] := a x + b x^2
Manipulate[Plot[f[x, a, b], {x, 0, 1}], {a, 0, 1}, {b, 0, 1}]

Image of Manipulate


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