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-intercepts of a Quadratic Function
The -intercepts of the function are the solutions of the quadratic equation . The solutions of a quadratic equation of the form are given by the quadratic formula.
Here, the expression is called the discriminant.
The discriminant can be used to confirm the number of -intercepts and the type of solutions of the quadratic equation.
Value of Discriminant |
Type and Number of
-intercepts (roots) |
Example of Graph of Related Function |
is a perfect square |
real and rational |
|
is not a perfect square |
real and irrational |
|
real |
|
|
No -intercepts |
|