SAT Math: Find the Maximum Value of f(x) = -2(x - 5)² + 18 in Under 5 Seconds

Exact Question Text

What is the maximum value of the quadratic function f(x) = -2(x - 5)^2 + 18?

1. Step-by-Step Formal Solution

1. Vertex is (h, k) = (5, 18).
2. (x - 5)^2 >= 0 for all real x, so -2(x - 5)^2 <= 0.
3. Maximum occurs at x = 5 where f(5) = 18.

2. Fast Desmos / Calculator Shortcut

Graph f(x) = -2(x - 5)^2 + 18 and click the top grey vertex point: (5, 18). Maximum value is y = 18.

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.