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The discriminant of the quadratic equation and parabola

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When using the quadratic formula to solve a quadratic equation ax^2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )

Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant.
You have to show at least two appropriate equation, compute the discriminant, and explain the resultant graph (for example, how is the x-axis intersected by the graph with a zero discriminant?).

In the real world, where might these imaginary numbers be used?

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Solution Summary

The solution elaborates on the relationship of the discriminant and the quadratic equation. It further explains how to judge the graph of the parabola based on the value of the discriminant. Supplemented with graphs and step-by-step texts, the solution provides a clear understanding of the meaning of the discriminant of the quadratic equation.

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(1) If the discriminant is zero, there is a repeated solution x, and this solution is real. Geometrically, ...

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