# 6: Solving Equations and Inequalities

- Page ID
- 6274

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- 6.1: Extracting Square Roots and Completing the Square
- Quadratic equations can have two real solutions, one real solution, or no real solution—in which case there will be two complex solutions.

- 6.2: Quadratic Formula
- In this section, we will develop a formula that gives the solutions to any quadratic equation in standard form.

- 6.3: Solving Equations Quadratic in Form
- Use the coefficients of a quadratic equation to help decide which method is most appropriate for solving it. While the quadratic formula always works, it is sometimes not the most efficient method.

- 6.4: Quadratic Functions and Their Graphs
- A quadratic function is a polynomial function of degree 2 which can be written in the general form, f(x)=ax²+bx+c.

- 6.5: Solving Quadratic Inequalities
- A quadratic inequality is a mathematical statement that relates a quadratic expression as either less than or greater than another. A solution to a quadratic inequality is a real number that will produce a true statement when substituted for the variable.

- 6.6: Solving Polynomial and Rational Inequalities
- A polynomial inequality is a mathematical statement that relates a polynomial expression as either less than or greater than another. We can use sign charts to solve polynomial inequalities with one variable.