Question

Using the graph as your guide, complete the following statement.

The discriminant of the function is ____.

Answer 1

By definition, the roots of a quadratic function can be found using an equation of the form:

`x = (-b+/-√(b^2 - 4ac))/(2a)`
The discriminant is the following part of the expression:

`b^2 - 4ac`
Therefore, we have three cases:

Case 1:

`b ^ 2 - 4ac\ \textgreater \ 0`
Then there are two real solutions

Case 2:

`b ^ 2 - 4ac = 0`
Then there is a real solution with multiplicity two

Case 3:

`b ^ 2 - 4ac \ \textless \ 0`
There are no real solutions

When the graph of a quadratic equation has no cut points with the x axis, then we are in case number 3.

Answer:
B. Negative

`b ^ 2 - 4ac \ \textless \ 0`