16
AssignmentMultiple Select

Quadratic Functions: Factored Form

Question 16 • AL-Algebra I with Probability Critical Standards

Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply.

Answer
A
The domain is all real numbers.
B
The range is all real numbers greater than or equal to 1.
C
The y-intercept is 3.
D
The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2.
E
The graph has two x-intercepts.

Explanation

The squared term is defined for every real x, so the domain is all real numbers. The graph has vertex (-1, 2), making its minimum value 2; therefore its range is y ≥ 2, not y ≥ 1. At x = 0, f(0) = (0 + 1)² + 2 = 3, so the y-intercept is 3. The graph shifts 1 unit left and 2 units up, and it has no x-intercepts.

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