Let's run this method with this example:

def g(x): return -np.exp(-x)*np.sin(x)
f = np.vectorize(lambda x: max(1-x, 2+x))
print (good_bracket(f, [-1, -0.5, 1]))
print (minimize_scalar(f, bracket=[-1, -0.5, 1], method=parabolic_step))

True
  fun: array(1.5000021457670878)
 nfev: 33
  nit: 11
    x: -0.50000214576708779

print (good_bracket(g, [0, 1.2, 1.5]))
True

print (minimize_scalar(g, bracket=[0,1.2,1.5], method=parabolic_step))

 fun: -0.32239694192707452
 nfev: 54
  nit: 18
    x: 0.78540558549352946

There are two methods already coded for univariate scalar minimization, golden, using a golden section search, and brent, following an algorithm by Brent and Dekker:

minimize_scalar(f, method='brent', bracket=[-1, -0.5, 1])
     fun: array(1.5)
    nfev: 22
     nit: 21
 success: True
       x: -0.5

minimize_scalar(f, method='golden', bracket=[-1, -0.5, 1])
     fun: array(1.5)
    nfev: 44
     nit: 39
 success: True
       x: -0.5

minimize_scalar(g, method='brent', bracket=[0, 1.2, 1.5])
     fun: -0.32239694194483448
    nfev: 11
     nit: 10
 success: True
       x: 0.78539816017203079

minimize_scalar(g, method='golden', bracket=[0, 1.2, 1.5])
     fun: -0.32239694194483448
    nfev: 43
     nit: 38
 success: True
       x: 0.7853981573284226