5
practice testMultiple Choice

Practice Test

Question 5 • Algebra: Concepts and Connections

Gerald graphs the function f of x is equal to x negative 3 squared negative 1 Which statements are true about the graph? Choose three correct answers.

Answer
A
The axis of symmetry is x is equal to negative 1 .
B
The vertex is 3 comma negative 1 .
C
The function decreases over the interval open paren negative infinity comma 3 close paren .
D
The domain is start set x such that x is greater than or equal to 3 end set .
E
The range is start set y such that y is greater than or equal to negative 1 end set .

Explanation

The function is f(x) = (x − 3)² − 1, which is in vertex form. Its vertex is (3, −1), and because the squared term has a positive coefficient, the parabola opens upward: it decreases until x = 3 and increases afterward. Its minimum y-value is −1, so the range is y ≥ −1; the domain is all real numbers, and the axis of symmetry is x = 3.

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