Problem 1 · Complete the square · 3 points
Made by AI and not reviewed by a real person.
What is the minimum value of x² − 6x + 11?
- 5
- 3
- −2
- 11
- 2
Show a hint
- Think of the expression as a graph. What feature of an upward-opening parabola marks its minimum, and how could you locate that feature?
- For y = x² + bx + c, the axis of symmetry is x = −b/2. Use it to find the vertex, then evaluate the expression there.
Show the answer and solution
Answer: E — 2
The coefficient of x² is positive, so the parabola opens upward and its vertex gives the minimum value. Its axis of symmetry is x = −(−6)/2 = 3. At x = 3, the expression is 3² − 6(3) + 11 = 2, so the correct choice is 2. The choice 3 is the x-value where the minimum occurs, not the minimum value.