Question

What is the maximum number of turns for the graph of f(x)=-x^4+3x^2

Answer 1

I assume by turns you mean turning points (otherwise considered as relative maxima or minima)?

Answer 2

yes

Answer 3

ok well you can start with theory.
A polynomial of degree n has a maximum of n-1 turning pts.

Now we go to the specifics.
Factorise your expression and sketch.

Or you can differentiate.

Answer 4

so is it 3 because when you graph it it looks like this: