Question

if the roots of ax^2+bx+c=0 are real, rational, and equal, what is true about the graph of y= ax^2+bx+c?
1.) it intersects the x-axis at 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

i think the answer is choice 1 but i'm not quite sure. can you please help me?

Answer 1

no
for 1.) the roots would have to be real, but different

The graph will intersect at the roots
since the roots are equal, the graph will have two equal intersection points, or in other words, it will just touch the x-axis.
so it must be tangent to the x-axis, thus 4)

Answer 2

Thank you once again!!! :)