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Important Rules About Zeros

OK!  First of all, a "zero" is where a graph crosses or touches the x-axis.

They're called "zeros" because that's where y = 0 !

graph of the two zeros of a parabola...where the graph crosses the x-axis and where y = 0

graph of a 3rd degree polynomial that touches the x-axis 2 times, or, has two zeros

*Officially, these are called "real zeros".

Here are some questions for you:

Can we draw a parabola (a 2nd degree polynomial) that

touches the x-axis twice?

graph of a 2nd degree polynomial that touches the x-axis twice

touches the x-axis once?

graph of a 2nd degree polynomial that touches the x-axis once

never touches the x-axis?

graph of a 2nd degree polynomial that never touches the x-axis