80570
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Quadratic Functions: Vertex Form

Question 80570 • * FL-1200315-Algebra 1 Sem 2 - CR

Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply.The domain is all real numbers. The range is all real numbers greater than or equal to 1.The y-intercept is 3.The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2.The graph has two x-intercepts.

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 function is f(x) = (x + 1)² + 2, a parabola that opens upward. Any real number can be used for x, so its domain is all real numbers. At x = 0, f(0) = 1² + 2 = 3, so the y-intercept is 3. Its minimum value is 2, not 1, and it has no x-intercepts; the graph is shifted 1 unit left and 2 units up.

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