In [1]: 
import numpy as np
import numpy.linalg as la
In [2]: 
alpha = 3
beta = 2
gamma = 2

def f(x):
    return alpha*x**2 + beta*x + gamma

plot_grid = np.linspace(-3, 3, 100)

plot(plot_grid, f(plot_grid))
Out[2]:
[<matplotlib.lines.Line2D at 0x4231890>]
In [3]: 
npts = 5

np.random.seed(22)
points = np.linspace(-2, 2, npts) + np.random.randn(npts)
values = f(points) + 0.3*np.random.randn(npts)*f(points)

plot(plot_grid, f(plot_grid))
plot(points, values, "o")
Out[3]:
[<matplotlib.lines.Line2D at 0x409be50>]
In [4]: 
A = np.array([
    np.ones(npts),
    points,
    points**2
    ]).T
print A

[[ 1.         -2.09194992  4.37625447]
 [ 1.         -2.46335065  6.06809644]
 [ 1.          1.08179168  1.17027324]
 [ 1.          0.76067483  0.5786262 ]
 [ 1.          1.50887086  2.27669128]]
In [6]: 
x = ...
x
Out[6]:
array([ 0.13178048,  1.84869187,  3.45132033])

(Edit this cell for solution.)

In [7]: 
... = x

def f_c(x):
    return alpha_c*x**2 + beta_c*x + gamma_c

plot(plot_grid, f(plot_grid), label="true")
plot(points, values, "o", label="data")
plot(plot_grid, f_c(plot_grid), label="found")
legend()
Out[7]:
<matplotlib.legend.Legend at 0x4773dd0>

(Edit this cell for solution.)