You can move from the second form to the first by expanding; you can move from the first to the second by completing the square or by using these formulas:
If (as we assume) it's not linear, then the graph of a quadratic function is a shape called a parabola. The point (h, k) on the graph is called the vertex of the parabola. If a > 0, then the vertex gives the absolute minimum of the function; if a < 0, then the vertex gives the absolute maximum of the function. (That is, the absolute minimum or maximum is k, and this absolute extremum occurs at h.) The parabola is symmetric, with a vertical line of symmetry whose equation is x = h. The vertical intercept, or y-intercept, on the graph is (0, c). The roots (or zeroes) of the function (which correspond to the horizontal intercepts, or x-intercepts, on the graph) are given by the quadratic formula:
In general, there are up to 7 useful points on the graph:
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