The equation of parabola is [tex]y=\frac{1}{10}\left(x-1\right)^{2}-2[/tex]
Comparing with the vertex form of the parabola: [tex]y=a(x-h)^2+k[/tex]
[tex]a=\frac{1}{10},h=1,k=-2[/tex]
Hence, the vertex of the parabola is given by (h,k) = (1, -2)
Now, vertex is the midpoint of the focus and the point on the directrix.
Distance, between vertex and focus is p and that of point on the directrix is p.
Now, let us find p
[tex]p=\frac{1}{4a}\\\\p=\frac{1}{4\cdot1/10}\\\\p=\frac{5}{2}[/tex]
Thus, the focus is given by
[tex](h,k+p)\\\\=(1,-2+5/2)\\\\=(1,1/2)=(1,0.5)[/tex]
And the directrix is given by
[tex]y=k-p\\\\y=-2-5/2\\\\y=-\frac{9}{2}[/tex]
Since, a >0 hence, it is an upward parabola.
The graph is shown in the attached file.
