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: