Chapter 1.8, Problem 52E

Solution

To find: Whether the discriminant of the quadratic function $a{x}^2+bx+c=0$ is positive, negative or zero for the graph shown.

  

The discriminant of the quadratic function is positive.

Given:

The graph of the quadratic function $a{x}^2+bx+c=0$ is shown below.

  

Concept used:

If the quadratic function $a{x}^2+bx+c=0$ cuts $x-$ axis at two different points, then the quadratic function has two real distinct solutions and it has positive discriminant.

Calculation:

From the graph it can be interpreted that the graph of the quadratic function $a{x}^2+bx+c=0$ cuts $x-$ axis at two different points. Therefore, the quadratic function has two real distinct solutions.

Hence, the discriminant of the quadratic function is positive.