QUIZ 3. Cool Quadratics
Let's say if function \(f(x)\) in domain \(\mathbb{R} \rightarrow \mathbb{R}\) satisfies all following conditions, then let's call \(f\) as "cool quadratic".
- \(f(x)\) is a quadratic polynomial.
- \(f''(x) \le 0\).
In other words, \(f(x) = ax^2 + bx + c\) and \(a < 0\).
You are going to draw \(n\) cool quadratics in \(2\)-dimensional plane. How many different areas can you create with \(n\) cool quadratics? For example, if \(n = 2\), then you can create up to \(5\) areas as drawn below.
Formula
- The red line is drawn by \(f(x) = -x^2 + 10\).
- The blue line is drawn by \(f(x) = -\frac{1}{2}x^2 + 7\).
Both functions are cool quadratics, satisfying all conditions above.
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