f(x)=x2-2x-8=(x-4)(x+2).
f(x)=0 when x=4 and when x=-2. f(x)=0 is the x-axis, so the curve (a parabola) intersects the x-axis at -2 and 4 on the x-axis. The x2 term is positive so the parabola is upright (U-shaped) and passes through (-2,0) and (4,0). These facts should enable you to identify the graph in a set of pictures. The vertex lies midway between the x-intercepts. The midway point is x=(4-2)/2=1. f(1)=1-2-8=-9. This makes the vertex, the lowest point on the parabola (minimum), the point (1,-9).