Given the following graph, define a) the vertex, b) the intercepts, c) the axis of symmetry, and the sign of the lead coefficient.

Vertex;

(2, -8)

The intercepts;

x-intercepts: (-2, 0) and (6, 0)

y-intercepts: (0, -6)

The axis of symmetry;

No axis of symmetry. X = 2 is a line of symmetry of the parabola

The sign of the lead coefficient;

Positive

Step-by-step explanation:

The graph shown in the attachment belongs to the parabola group of conic sections. The vertex of a parabola refers to the point where the parabola changes direction or also the lowest or the highest point on its graph. The graph is moving downwards from x = -4 to x = 2 and then starts moving upwards from x = 2 to x = 8. The vertex is thus located at the point x = 2. At this point, the y value is -8. Thus the vertex is located at (2, -8). This is the lowest point on the graph.

The intercepts refers to the points where the graph of a function crosses or cuts either the x or the y axes.

The parabola crosses the x-axis at two points;

x = -2 and x = 6

At these points the value of y is usually 0. The x-intercepts are thus;

(-2, 0) and (6, 0)

The parabola crosses the y-axis at the point where y = -6 and the corresponding x value is 0. The y-intercept is thus;

(0, -6)

Neither the x-axis nor the y-axis is an axis of symmetry of the parabola since neither of the axis divides the parabola into two identical portions. Nevertheless, the vertical line x = 2 passing through the vertex divides the parabola into two identical portions such that the left portion is a mirror image of the right portion. We can thus conclude that the vertical line x = 2 is a line of symmetry of the parabola.

The sign of the lead coefficient of a parabola determine whether the parabola opens upward or downward;

If the sign of the lead coefficient is positive, the parabola opens upward. If the sign of the lead coefficient is negative, the parabola opens downward.

The parabola in the attachment opens upward and thus the sign of its lead coefficient is positive.