The discriminant's role in quadratic equation solutions and graphs

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Quadratic Formula

Info: 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. (When the discriminate 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 = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.

Search the Cybrary and Internet. In the real world, where might these imaginary numbers be used?

The discriminant b2-4ac is used to identify three possible solution cases for quadratic equations: one real solution, two real solutions, and an imaginary solution. For the first case (one real solution), it will show a parabola that touches the x-axis at a single point. For example, the equation y = x^2-2x + 1 will produce the following graph:

For this case, the discriminant is b^2-4ac = -2^2-4*1*1 = 4-4 = 0. The parabola touches the x-axis at a single point (2, 0), which is the solution if y = 0. For the second case (two real solutions), it will show a parabola that touches the x-axis at two points. For example, the equation y = x^2-3x + 2 will have the following graph: