# 7.1 Quadratic Equations; Solution by Factoring

**General Quadratic Equation • Solutions of a Quadratic Equation • Solving a Quadratic Equation by Factoring • Equations with Fractions**

*Given that a, b, and c are constants* $(a\hspace{0.17em}\ne \hspace{0.17em}0)\hspace{0.17em},\hspace{0.17em}$ *the equation*

**(7.1)**

*is called the* **general quadratic equation in x.** The left side of Eq. (7.1) is a polynomial function of degree 2.

*This function,*$f(x)\hspace{0.17em}=\hspace{0.17em}a{x}^{2}\hspace{0.17em}+\hspace{0.17em}bx\hspace{0.17em}+\hspace{0.17em}c\hspace{0.17em},\hspace{0.17em}$

*is known as the*

**quadratic function.**Any equation that can be simplified and then written in the form of Eq. (7.1) is a quadratic equation in one unknown.

Among the applications of quadratic equations and functions are the following examples: In finding the flight time `t` of a projectile, the equation ${s}_{0}\hspace{0.17em}+\hspace{0.17em}{v}_{0}t\hspace{0.17em}-\hspace{0.17em}16{t}^{2}\hspace{0.17em}=\hspace{0.17em}0$ occurs; in analyzing ...

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