Quadratic functions are very commonly used both in an Algebra course and in the real world. In this section, the topics of equations, functions, graphs, word problems, and various other topics involving quadratics will be explored.

Learn how to solve quadratic equations utilizing many different techniques. The quadratic formula can be used to solve all quadratic equations. Factoring quadratic equations can only be used if the function is factorable. If the linear term is missing, the square root method can be used.

Solve by Factoring Ex 1

Solve by Factoring Ex 2

Solve by Factoring Ex 3

Solve by Square Root Method

Solve Using the
Quadratic Formula Ex 1

Quadratic Formula
No Real Solutions

Throwing a Ball from a Building Application

Graphs

Learn how to graph quadratic functions using different techniques. Techniques include using transformations of the parent function, finding the vertex and intercepts, and graph using intercepts when the vertex is on the x-axis. The graph is called a parabola. A parabola can open up and have a minimum point, or the graph can open down and have a maximum. The domain is always all real numbers, and the range depends on the direction of opening and the location of the vertex.

Graph a Quadratic in Vertex Form Using Translations

Vertical Stretches or Compressions of Quadratic Graphs

Using Vertex and Intercepts to Graph

Using Intercepts to Graph a Quadratic Function

Graph a Parabola Using Vertex and Intercepts (down)

Functions

Quadratic functions are functions that are degree 2 polynomials. That means the highest exponent on a variable is two. Function notations is useful, because then you know what you plugged in for x to get the output. In some Algebra courses, you will have to find the quadratic function that passes through a given point with a given vertex.

Find the Function with the Given Vertex and y-intercept

Find the Function with the Given Vertex and a Point

Extrema

Extrema are the extreme points of a graph. They are the maximum and/or minimum points of a graph. All quadratic functions either have a maximum value or a minimum value. The maximum occurs if the parabola opens downward, and the minimum occurs if the parabola opens upward. The maximum or minimum occur at the vertex (turning point) of the graph. The maximum or minimum is the y-coordinate only.