Question

question 17 of 23
1 point
what does the discriminant tell you?
select the correct response:
how many and what kind of solutions are possible.
how many y - intercepts a parabola has.
whether the parabola opens up or down.
how many and what kind of solutions are possible.
how many x - intercepts a parabola has.
whether the parabola opens up or down. how many y - intercepts the parabola has.

Explanation:

The discriminant of a quadratic equation \( ax^{2}+bx + c = 0\) (where \(a
eq0\)) is given by \(D=b^{2}-4ac\). If \(D>0\), there are two distinct real solutions (or two \(x\)-intercepts for the parabola \(y = ax^{2}+bx + c\)); if \(D = 0\), there is one real solution (or one \(x\)-intercept); if \(D<0\), there are no real solutions (or no \(x\)-intercepts). Also, the nature of the solutions (real and distinct, real and equal, or complex) is determined by the discriminant. The number of \(y\)-intercepts of a parabola is always 1 (since when \(x = 0\), \(y=c\)), and the direction the parabola opens (up or down) is determined by the coefficient \(a\) (positive for up, negative for down), not the discriminant. So the correct description related to the discriminant is about how many and what kind of solutions (and also related to \(x\)-intercepts as \(x\)-intercepts are the real solutions) are possible.

Answer:

How many and what kind of solutions are possible.
How many x - intercepts a parabola has.