Question

Which of the following sjows the correct key features of the graph?

Answer 1

Answer:

Step-by-step explanation:

y = x^2 - x - 2 is a quadratic function.  It's easily factorable:  y = (x + 1)(x - 2).  Setting this result equal to zero yields the x-intercepts:  -1 and 2.  This matches the x-intercepts shown on the graph.

The axis of symmetry,  x = -b/(2a), derived from the coefficients 1, -1 and -2 of this particular function, is x = 1/2.  This x = 1/2 is also the x-coordinate of the vertex.  To find the y-coordinate of the vertex, we evaluate y = x^2 - x - 2 at x = 1/2, obtaining:

y = (1/2)^2 - (1/2) - 2, or y = 1/4 - 1/2 - 2, or -2 1/4.  This does not quite agree with the y value (-2) shown in the diagram, but is close.