The equation y = 2(x - 1)2 – 5 is graphed in the xy-plane. Which of the following statements about the graph is true?

 The equation given is y = 2(x - 1)^2 - 5, which is an example of a parabola in vertex form. The vertex form of a parabola's equation is generally expressed as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this form, 'a' determines the width and direction of the opening of the parabola.

Analyzing the given equation:

1. The coefficient "a" is 2, which means that the parabola opens upwards (since 'a' is positive) and is vertically stretched (since |a| > 1). 2. The expression (x - 1) indicates that the vertex has moved to the right by 1 unit from the origin. 3. The constant term "-5" shows that the vertex is also shifted downward by 5 units.

Therefore, the vertex of the parabola is (h, k) = (1, -5). Since 'a' is positive, the parabola opens upwards, and the vertex represents the lowest point, or the minimum, of the parabola.

Extra: Understanding parabolas is a fundamental part of algebra and pre-calculus curricula, and recognizing their key features is crucial. A parabola is a U-shaped graph that can open upwards or downwards. If the coefficient 'a' in the vertex form is positive, it opens upwards, meaning it has a minimum point; if 'a' is negative, it opens downwards, meaning it has a maximum point. The vertex of the parabola is an important feature: it is the turning point where the graph changes direction. The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two symmetrical halves. Lastly, the parabola's domain is all real numbers, but its range depends on whether it opens upwards or downwards and where the vertex is located.