Graphing Quadratic Functions

 A quadratic function is a polynomial of degree 2 and its graph is a parabola. 

 

 

Roots - The roots, or “zeros,” of a function are the values of x that make the function equal to zero.  A quadratic function always has two roots but it doesn't always have two x-intercepts.  The nature of its roots can tell you about what the graph looks like. 

 

Finding the Roots of a Quadratic Function – We have learned three different methods for finding the roots of a quadratic function.  All three start with the same first step... let y = 0 and solve for x!  The three methods are factoring, completing the square and the quadratic formula.  Check out these notes for a detailed description of each method.

 

The Discriminant (a.k.a What a Function's Roots Tell you about Its Graph) - A quadratic function has two roots and you can find out what type of roots they are by using the discriminant = .