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parabola

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First Part:

What is the discriminant? Explain what information the discriminant gives us and why this information is important. What does the discriminant tell us about the graph of a quadratic equation?

Second Part:

What is a parabola and where does it come from? What important information is given by the vertex of a parabola? How do we determine if a parabola has a maximum or a minimum value?

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Solution Summary

Discriminants and parabolas are defined and exemplified.

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For the quadratic equation ax^2+bx+c=0 the discriminant is the number
D=b^2-4ac

Since in the quadratic formula,

x=[-b + sqrt(D)] / (2a), x=[-b - sqrt(D)] (2a)

used to find the solutions to the quadratic equation the discriminant is under the square root, if it's negative, the equation does not have any real solutions. If the discriminant is zero, the expressions above become identical, so if D=0, the equation has ...

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