The equation y = 2(x - 1)2 - 5 is graphed in the xy-plane. Which of the following statements about the graph is true?
A. It is symmetrical about the line y = 1
B. It is symmetrical about the line x = 1
C. Its vertex occurs at the point (-1, -5)
D. Its vertex occurs at the point (2, -5)
The vertex of the graph of any quadratic equation in the form y = a(x - h)2 - k is the point (h, k).
Thus, in the given equation, the vertex is (1, -5)
Also, we know that a parabola's axis of symmetry always goes through the vertex of the parabola. In other words, it is a vertical line that goes through the x-coordinate of the vertex and the x cordinate of the vertex is 1.
Therefore, the parabola is symmetrical about the line x = 1
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