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Finding the Discriminant in a Quadratic Equation

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what this value means to the graph of y = ax2 + bx + c.

Solution Preview

Please see the attached file for the complete solution.

Solution:

For ax^2 + bx + c = 0, the value of x is given by:

see attached

If discriminant is b^2 - 4ac=0, then x=-b/2a

If discriminant is b^2 - 4ac>0, then (see attached)

If a quadratic equation with real-number coefficients has a negative discriminant, ...

Solution Summary

Discriminants are investigated. The solution is detailed and well presented.

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