How do you find the discriminant on a graph?

Answer 1

The discriminant is the expression under the square root of the quadratic formula.

For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:

• x = (-b +- sqrt(b2 - 4ac)) / (2a).

So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.

• (b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.
• (b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.
• (b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.

So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.