Math 137 Module 14 Intro to Quadratic Functions
Definition:
A quadratic function is of the form: 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 where a, b, and c are real numbers (with a≠0).
The graph of a quadratic function is called a parabola.
Example 1
The graph below shows the graph of the quadratic function: 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 1
Note that the parabola opens up and has a lowest point at (2, - 3). Since a = 1 which is positive, the
graph will open up. The lowest point is called the vertex.
−𝑏
The x-coordinate of the vertex can be found by using the following formula: = 2𝑎 . The y-coordinate can
then be found by plugging in the x value found.
Example 2
The graph below shows the graph of the quadratic function: 𝑓(𝑥) = −2𝑥 2 + 4𝑥 + 3
Note that the parabola opens down and has a highest point at its vertex (1, 5). Since a = - 2 is negative,
the graph will open down.
Let’s find the vertex using the quadratic function: