Luke 

The discriminate in the quadratic formula  is used to find the 2 roots of the x- intercept.  When you have a negative you will have no X- intercepts but you will have an imaginary x intercept because it'll be above the line and won't be touching the X axis, If you have 2 different real roots then you will have two x intercepts, and if you have two identical real roots then you will only have 1 x-intercept because it will jsut be touching the x axis at 0 causing it to have 1 X-Intercept.  With using the Quadratic formula you will always have 2 roots, but in some cases you will not have 2 x-intercepts.

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