Cue Column:

• Both roots > k?
• Both roots < k?
• k between roots?
• Both roots in interval?

Note Column: For $ax^2$ + bx + c = 0, a > 0, roots alpha, beta:

1. Both roots > k: D >= 0 AND f(k) > 0 AND -$\frac{b}{2a}$ > k
2. Both roots < k: D >= 0 AND f(k) > 0 AND -$\frac{b}{2a}$ < k
3. k between roots: f(k) < 0 (this alone is sufficient!)
4. Both roots in (p,q): D >= 0 AND f(p) > 0 AND f(q) > 0 AND p < -$\frac{b}{2a}$ < q
5. Exactly one root in (p,q): f(p)*f(q) < 0

Summary: Location conditions combine three tools: discriminant, function value at key points, and vertex position. Condition 3 is the simplest — just one inequality.