# Solving Quadratic Equations and Inequalities

## Vocabulary

### completing the square

process used to rewrite a quadratic expression as the sum of a perfect square trinomial and a constant

### discriminant

$b^2-4ac$

### factoring

process of writing a number or algebraic expression as a product

polynomial equation, where $a$, $b$, and $c$ are real numbers and $a\neq 0$, that can be written in the form:
$ax^2 + bx + c = 0$

formula used to solve a quadratic equation of the form $ax^2+bx+c=0$ by using its coefficients:
$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

mathematical statement that compares a quadratic expression of the form $ax^2 +bx + c$ to another expression or value using the symbols $<$, $>$, $\leq$, or $\geq$

### solution of an equation

value of the variable that makes the equation true, which means both sides are equal

### solution of an inequality

value of the variable that makes the inequality true, which means the comparison is valid

### x-intercept

value of $x$ where a graph touches or crosses the $x$-axis

### zero of a function

any input value of a function that makes the output of the function equal to zero