Section 4.1 - Quadratic Functions and Applications

Section Objectives

  1. Find the vertex, intercepts, and symmetry axis of a parabola.
  2. Write a quadratic function in vertex form.
  3. Find the equation of a quadratic function from its graph.
  4. Solve application problems involving quadratic functions and parabolas.



Quadratic functions

A quadratic function is a 2nd degree polynomial function. Every quadratic function can be written in the standard form , where , , and are real numbers with .



The graph of a quadratic function is a smooth U-shaped curve called a parabola. The turning point at the tip of the U is called the vertex, and the graph is symmetric about the vertical line through the vertex.




By completing the square, any quadratic function in standard form, , can be rewritten in the equivalent vertex form

.




Examples