For what value of x does f(x) = (x - 3)² reach its minimum?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Study for the PSAT 8/9 Math Test. Practice with flashcards and multiple choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

For what value of x does f(x) = (x - 3)² reach its minimum?

Explanation:
The smallest value of a square happens when the inner expression is zero. For f(x) = (x - 3)^2, the inside is zero when x = 3, giving f(3) = 0. Since a square is never negative, 0 is the minimum possible value, and it occurs at x = 3. Any other x makes (x - 3)^2 positive, so they don’t minimize f. So the minimum occurs at x = 3.

The smallest value of a square happens when the inner expression is zero. For f(x) = (x - 3)^2, the inside is zero when x = 3, giving f(3) = 0. Since a square is never negative, 0 is the minimum possible value, and it occurs at x = 3. Any other x makes (x - 3)^2 positive, so they don’t minimize f. So the minimum occurs at x = 3.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy