How to Find Quadratic Functions From a Graph Not Crossing the X Axis

How to find quadratic functions from a graph, not crossing the X axis? I'm Bon Crowder with MathFour.com, and we're looking at how to find the quadratic function from a graph where it doesn't cross the X axis. So, what we have here, is a quadratic, a parabola, with vertex at two, one, through the point three, four. From this information, we can plug it into this form which says that F of X for the function here, is A times X minus H. And here H and K are the pieces of vertex, here's H, K. So, this is X minus two squared plus K, which is one. So, that's almost where we want to be. The problem is, is we need to know what this A is. The other piece of information we have, is this point three, four. So, we know that F of three is the same as four. So, we can plug in three for X and we know that this is four. So, I do three minus two, is one squared, doing a little handy arithmetic. This is A plus one, subtract my one and it turns out that A is three. So, now I can go back and say, F of X is three, X minus two squared plus one. And now, I've found the formula for my quadratic, given a graph that doesn't cross the X axis. I'm Bon Crowder with MathFour.com, have fun with it.