Introduction

Discriminant

The discriminant is the part of the quadratic formula under the radical.

x equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a. c and denominator 2 a.

What does the word discriminate mean? Discriminate means make a difference in.

If you say 22° you think, "Cold" and if I say 99°, you think "Hot" without me saying another word.

The discriminant is another number that tells us something about a quadratic equation.

If the discriminant is the part of the quadratic formula under the radical, what would the formula of the discriminant be?

Answer: D = b2 − 4ac

Discriminant Example

Let's work an example: Find the discriminant of 3x2 + x + 9 = 0

First, list a, b, c.

  1. 3
  2. 1
  3. 9

Plug these values into the formula:

  • D = b2 − 4ac
  • D = 12 − 4(3)(9)
  • D = ___blank

Answer:

  • D = −107

Now, graph the related quadratic function, y = 3x2 + x + 9. We see that the quadratic function does not cross the x-axis which means the x-intercepts are imaginary. Note also that the value of the discriminant is negative.

Empty graph with x and y axis. Graph size displayed from negative 8 to 9 on the x axis and negative 2 to 19 on the y axis.

There are no x-intercepts, the y-intercept is 9 and the solutions are imaginary.

A coordinate plane with a graph of a parabola or u shaped graph opening up with a vertex at (0, 9). The graph is above the x-axis opening up, so there are not any x-intercepts.