If the roots of ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function?

1. It intersects the x-axis in two distinct points.


2. It lies entirely below the x-axis.


3. It lies entirely above the x-axis.


4. It is tangent to the x-axis.If the roots of ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function?
4If the roots of ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function?
it is a parabola





1
the correct answer is 4.


It meets the x axis at only one point.





verify this yourself by plotting x^2 - 8x + 16


the roots are real, rational and equal.
Oops! Sorry guys! I marked one of the ';4'; answers thumbs down.


If the two roots are equal, the quadratic is of the form (x卤鈭歝)(x卤鈭歝) with roots, x= +鈭歝 or -鈭歝 but NOT both.


Since the equation intercepts the x-axis at only one point, it IS tangent at that point. That is, the graph is tangent to the x-axis at the interception (but NOWHERE else). I was thinking 4 implied the the graph was a tangent line...