Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that
\[f(x) f(-x) = f(x^2).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that
\[f(x) f(-x) = f(x^2).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that
\[f(x) f(-x) = f(x^2).\]
train