JAMB 2010 Mathematics · Question 36

At what value of X does the function y = -3 - 2x + X2 attain a minimum value?

Options

A.-1
B.14
C.4
D.1

Answer: D. 1

Explanation written with AI and checked against the answer key

Analyze the question: We need the value of x at which the quadratic y = x² − 2x − 3 reaches its minimum. (The "X2" in the question is read as x², which is the standard form of this JAMB question.) Concept: For a quadratic y = ax² + bx + c with a > 0, the graph opens upward, so it has a minimum. The minimum occurs where dy/dx = 0, or at the vertex x = −b/(2a). Solution: Write the function in standard form: y = x² − 2x − 3 Here a = 1, b = −2 and c = −3. Since a > 0, there is a minimum. Method 1: Differentiation dy/dx = 2x − 2 Set dy/dx = 0: 2x − 2 = 0, so x = 1. Check: d²y/dx² = 2 > 0, so this is a minimum. Method 2: Vertex formula x = −b/(2a) = −(−2)/(2×1) = 1 Check by substitution: At x = 1: y = 1 − 2 − 3 = −4 At x = 0: y = −3 (higher) At x = 2: y = 4 − 4 − 3 = −3 (higher) So x = 1 gives the lowest value, y = −4. Answer: The minimum occurs at x = 1, which is option D. Tip: For any quadratic ax² + bx + c, the turning point is always at x = −b/(2a). If a is positive it is a minimum, and if a is negative it is a maximum. This lets you answer in seconds without differentiating.

AI can make mistakes. Report anything that looks wrong.