Discriminant Cases
Move the slider — does the parabola hit the x-axis once, twice, or not at all?
y
=
x
² +
c
x
y
−4
−2
2
4
−4
−2
2
4
6
8
10
DISCRIMINANT
D
= 0
D = b² − 4ac
SLIDER
c
= 0
CASE
D = 0
One real root
(tangent to x-axis)
ROOTS
x = 0
The discriminant tells you how many times the parabola crosses the x-axis.
D
> 0: two roots.
D
= 0: one root.
D
< 0: no real roots.
−4
+4
Reset to c = 0