which function has a negative discriminant value?

Explanation:

Step1: Recall discriminant - parabola relation

The discriminant of a quadratic function (y = ax^{2}+bx + c) is (\Delta=b^{2}-4ac). If (\Delta<0), the quadratic function has no real - x - intercepts.

Step2: Analyze each graph

Examine the x - intercepts of each parabola. A parabola with no real x - intercepts has a negative discriminant.

• The first parabola crosses the x - axis at two points, so (\Delta>0).
• The second parabola crosses the x - axis at two points, so (\Delta>0).
• The third parabola crosses the x - axis at two points, so (\Delta>0).
• The fourth parabola does not cross the x - axis, so (\Delta < 0).

Answer:

The fourth function (the parabola that does not cross the x - axis)