1.3
Quadratic Functions
Definition 5 A quadratic function is a function that can be expressed in the
form
() = 2+ +
where and are constants and 6= 0.
(1)Show Graph
(2)Vertex
Theorem 1 The vertex of parabola that represents a function of the form
() = 2+ +
is the point whose coordinate is −
2
Proof. Use the symmetry of parabola. For example () = 052−3+55
052 − 3 + 55 5 2.5 0 -2.5 6.25 5 3.75 2.5 1.25 0 x y x y
(3)Maximum and Minimum Value ( Use the sign of and ¡−2¢)
Example 9 () = 0252
− 2 + 6
(4)Zero ( () = 0−±√22−4)
Example 10 () =−22+ 9− 4 92− 12 + 4 2− 6 + 10
(5)Polynomial function (degree , deg ( ()) =?)
