6
QuizMultiple Choice

Parabolas

Question 6 • Applications and Modeling

Find the domain and range of the function below. y = 3x2 - 6x + 5

Answer
A
D: all real numbers R: (y ≥ 2)
B
D: all real numbersR: (y ≤ 2)
C
D: (x ≥ 2)R: all real numbers
D
D: all real numbers R: all real numbers

Explanation

Rewrite the function by completing the square: y = 3x² − 6x + 5 = 3(x − 1)² + 2. Since x can be any real number, the domain is all real numbers. The squared term is never negative, so the smallest value of y is 2; the range is y ≥ 2. This matches choice A.

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