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A quadratic equation is one that has a "squared" term.  This is known as second degree or power of two.

These equations are usually put into one of two forms.

• Standard form:                  examples:             

• I call this perfect square form             examples:            

The graph of a quadratic equation is a called parabola.  It is sometimes referred to as a "U" graph.  It can open up or open down.   No part of this graph is straight and the slope is different for every combination of points you choose to evaluate.  (Recall that a line has consatnt slope.)

The parent graph for parabolas is the function				From looking at the parent graph, you can see that it could be shifted up or down from (0,0).
It is what we will compare other graphs to to call them wide or narrow, shifted up or shifted down.		click on the picture for a larger view of the graph		This would leave it centered on the x-axis, meaning it is symmetric about the y-axis, but moved up or down along the vertical axis.

  When looking at the perfect square form of the equation, you can see that this shift up or down would come from a value outside the squared term.  It is easiest to see this when a = 1 and h = 0.

  By order of operations, this means that the last thing calculated is the addition of "k".  If k is positive the shift is up.  If k is negative the shift is down.

examples:    is a shift up 2 units and is shifted down 2 units

For more work with the equations that graph as parabolas you can check out: quadratics2.htm