When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac.

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 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 = ax2 + bx + c. Hint: Choose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.


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

When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac.
Let the discriminant be D = b^2 - 4ac





If D = 0,


there will be equal roots to the equation (i.e one solution)


The graph will "touch" the x-axis at the stationary point of the curve.





If D %26gt; 0


discriminant is positive; equation has two distinct roots (two different solutions). Graph cuts x-axis at two points.





If D %26lt; 0,


discriminant is negative, equation has NO REAL solution (might have imaginary solutions). Graph does not intersect with x-axis.
Reply:if discriminant %26gt;0, the two roots are real and the graph(parabola) cuts the x axis in two points.


if the discriminant is zero, it has two equal roots, the x axis is tangent to the parabola, touches it at one point. if the discriminant is negative, the two roots are complexand the paraboladoes not have intersection with the x axis.