Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that
\[f(x) f(-x) = f(x^2).\]
Question:
Find the number of functions of the form $f(x) = ax^2 + bx + c$ such that
\[f(x) f(-x) = f(x^2).\]
Answer:
Let's think step by step.

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