I have another simple matplotlib example, based on the parabola post from the other day (here). The conclusion from that post was that any function:

can be manipulated to the form:

That is, the parabola is just

`y = a(x)`^{2}

translated to have a different vertex. I didn't do a systematic examination or anything, but here is one example in Python.The function

`quadratic`

takes arguments `a, b, and c`

and returns the vertex `(x`_{0}, y_{0})

as well as a numpy array containing `x`

such that `|x - x`_{0}| <= 4

, and a second one containing `f(x)`

for each value of `x`

.We plot two sets of three parabolas, each set has one for each of

`a = 1, 2 and 3`

. One set is at the origin (cyan, blue and purple). The second set (magenta, salmon and red) has `c = 3`

and:Since

`x`_{0} = -b/2a

is the same for each parabola in the second set, they all have the same axis of symmetry. The only difference (besides the shape parameter `a`

) is `y`_{0}

, which can be calculated either from plugging `a, b, c and x`_{0}

into the standard form, or by using the fact thatUsing the second method, I get:

We ought to be able to solve for b and c to put the parabola anywhere on the x,y-plane..

UPDATE: