import matplotlib.pyplot as plt
import numpy as np
N = 10
xmin = 0
xmax = 9
def f1(x):
   y = (-1) *( (1/2)*x*x ) + (4)*x
   if (y <= 0):
       return 0.0
   else:
       return y
def f2(x):
   return (-1) *( (1/4)*x*x ) + (5/2)*x
def f3(x):
   return (-1) *( (1/6)*x*x ) + (5/3)*x
p = np.linspace( xmin, xmax, N)
plt.plot( p, [f1(p[k]) for k in range(N)] )
plt.plot( p, [f2(p[k]) for k in range(N)] )
plt.plot( p, [f3(p[k]) for k in range(N)] )
plt.grid()
plt.plot([7.5, 8.3], [2.5, 2.5], linewidth=5)
plt.show()