Solve a Quadratic Equation: Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c.

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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