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

The discriminant of the function is ____.

Using the graph as your guide, complete the following statement. The discriminant-example-1
User Johnwargo
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1 Answer

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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
User Matthias Alleweldt
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