$($a$)$ Which of the four control points $($arbitrarily labeled $0$ through $3$ in the plot$)$ will the curve pass through, and for what values of $t?$

$($b$)$ Which control points affect the tangent to the curve at $t=0?$ At $t=1?$

$($c$)$ Does this spline have the convex hull property? How did you tell?