Value of Money Quadratic Formula

¶ … Value of Money 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: In this case, the discriminant is b^2-4ac = -3^2-4*1*2 = 9-8 = 1.

The parabola touches the x-axis at points (1, 0) and (2, 0), which are the two solutions when y = 0. For the third case (imaginary solution), it won't show a graph in the Cartesian plane unless we include the complex.