Quadratic Functions and Equations

In this chapter, we will look at quadratic functions, quadratic equations, and the solutions of quadratic equations.
Given that a, b, and c are constants and that $a \neq = 0,$ then a quadratic function is any function that can be written on the form $f (x) = a x^{2} + b x + c$ and a quadratic equation is any equation that can be written on the form $a x^{2} + b x + c = 0 .$
A quadratic equation can have zero, one, or two solutions when considering the real numbers only. When allowing for complex numbers, it can be shown that every quadratic equation has either one or two solutions.
When introducing complex numbers the imaginary unit, i, is defined. It is also explained how to perform arithmetic operations, including addition, subtraction, and multiplication, of complex numbers. There are several different methods to solve quadratic equations. Commonly used methods include square roots, factoring, and by using the Quadratic Formula.
Covered in this chapter is also methods for solving systems of quadratic equations and systems of quadratic inequalities. These methods include graphical methods and the Substitution Method.
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Subchapters:

Quadratic Functions and Equations

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