In this chapter quadratic functions are introduced and various aspects of them are explored.
The graphs of quadratic functions are analyzed by describing their characteristics. The characteristics studied are the direction of the parabola, the function's vertex, its axis of symmetry, zeroes, and y-intercept.
If the parabola of a quadratic function opens upward the vertex represents absolute minimum of the function and if the parabola opens downward the vertex is the function's absolute maximum.
In the chapter three different forms on how to write the function rules of quadratic functions are studied. These are standard form, vertex form, and factored form.
The axis of symmetry of a quadratic functions are vertical and passes through the vertex.
The advantage of the vertex form is that it allows for identification of the coordinates of the vertex by inspecting the function rule. To write the function rule in factored form is useful when it is necessary to identify the zeroes of the function. When the quadratic function is written in factored form the zeroes can be found without having to manipulate the function rule.
Lastly, the effects of transformations on quadratic functions are explored in both the rules and graphs of functions. The transformations that are studied are vertical translations, horizontal translations, reflections in the x-axis and the y-axis, and stretching and shrinking of the function.