Multiple choice

Which of the following is true about the quadratic function f(x) = x2 – 10x + 23?

  1. y ≥ -2

  2. y ≤ -2

  3. x ≥ 5

  4. x ≤ 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

f(x) = x^2 - 10x + 23. Complete the square: (x-5)^2 - 25 + 23 = (x-5)^2 - 2. The minimum value of the function is -2, so y >= -2.

AI explanation

Using the method of completing the square, the function f(x) = x2 - 10x + 23 becomes (x2 - 10x + 25) - 2. This simplifies to (x - 5)2 - 2. Because the square of a real number is always non-negative, the minimum value occurs when x = 5, making the minimum y equal to -2, so y is always greater than or equal to -2.

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