SOLUTION: in y=ax^2+bx+c i understand that b is a strong determinant of the x-intercepts of the curve, but can you explain that more to me? and please give examples if possible!

Question 70739: in y=ax^2+bx+c i understand that b is a strong determinant of the x-intercepts of the curve, but can you explain that more to me? and please give examples if possible!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The roots, or x-intercepts, are found by the formula

rewrite this as

The under the square root sign
determines the nature of the x-intercepts (roots).
If , the whole 2nd term is zero, and
there is 1 x-intercept at . All this
means is that the vertex of the parabola just kisses
the x-axis.
If , There are 2 x-intercepts at these locations:

and

If , There are a pair of imaginary roots
(involving )
All that means is that the parabola never touches the x-axis
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