Chapter 1.8, Problem 53E

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 negative.

Given:

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

  

Concept used:

If the quadratic function $a{x}^2+bx+c=0$ doesn’t cut $x-$ axis at any point, then the quadratic function has two real imaginary solutions and it has negative discriminant.

Calculation:

From the graph it can be interpreted that the graph of the quadratic function $a{x}^2+bx+c=0$ doesn’t cut $x-$ axis at any point. Therefore, the quadratic function has two imaginary solutions.

Hence, the discriminant of the quadratic function is negative.