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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 (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

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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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