Equations for factored, standard, and vertex form using a graph?

In the graph, you can just pick the coordinates.
Then, can make the equation like: y = x² - 5x + 6

Then, we can make the factors like:
y = x²-3x-2x+6
y = x(x - 3) -2(x -3)
y = (x-2)(x-3)
y = 2, 3

Then, we can convert it into standard and vertex form by applying appropriate steps, here for this particular example:
y - 6 = x² - 5x
y - 6 = x(x - 5)

[ Post your own particular question for better understanding ]

Hope this helps!