Hi, the videos on graphing quadratic functions gave me some new ideas but they don't cover all possible cases. How do you draw a quadratic function in standard form that has no intersections with the x-axis? I would use the method of completing the squares for it.This is covered somewhere else but the connection to the graph is not explained there.
Regards
Sabine
Hi Sabine,
If you are looking for an expression of a quadratic with no real zeros, you want to keep in mind that the answers for such an expression (the range) should either (a) always be positive, or (b) always be negative, and never equal zero. The general form of such a quadratic would be a curve that is either entirely above or entirely below the x-axis.
One way you can come up with one is to test values for a, b and c in the quadratic formula. Use numbers whereby the discriminant will be negative - this means that the quadratic in question has only complex roots. An example: a=7, b=15, c=10.
Hope this helps.
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