Digital SAT Math
Bluebook Test 4 Math Module 2 Question 20: y = 3x² - bx + 12 One x-Intercept
• Direct Answer / Key Takeaway
Delta = (-b)^2 - 4(3)(12) = 0 => b^2 = 144 => b = 12 (since b > 0).
Exact Question Text
In the xy-plane, the graph of y = 3x^2 - bx + 12 intersects the x-axis at exactly one point. If b > 0, what is the value of b?
1. Step-by-Step Formal Solution
- One x-intercept => Delta = 0.
- b^2 - 144 = 0 => b = 12.
- Option B is correct.
2. Fast Desmos / Calculator Shortcut
Type y = 3x^2 - bx + 12 with slider b = 12. Vertex touches (2, 0).
3. Distractor Trap Analysis
- Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
- Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
- Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
- Option Correct: Accurately satisfies all algebraic and logical constraints.
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