Glossary for Lesson 10: Parabolas

Parabola

A parabola is a curve shaped almost like a \union .  In this course, we will just look at parabolas that open either upward or downward on the coordinate plane.  As a result, the axis of symmetry, the line that divides the parabola equally in half, for each parabola we talk about will be a vertical line.  Parabolas of this sort have equations of the form y=ax^2+bx+c, where a , b , and c are constants and a is not equal to 0 .

Standard Form for the Equation of a Parabola

In this class, we will say that the equation of a parabola is in standard form if it is written in the form y=ax^2+bx+c , where a , b , and c are constants and a is not equal to 0

Factoring

When we factor a polynomial, we break it down so that it is written as a product of factors.  In this course, we will say that a polynomial is fully factored or completely factored when it is written as the product of factors with integer coefficients and none of its factors can be factored any further.  For example, (x-3)(x+1)(2x-5) is fully factored, whereas (3x+1)(x^2-1) is not because we could instead write it as (3x+1)(x-1)(x+1)

Quadratic Equation

A quadratic equation is an equation of the form ax^2+bx+c=0 , where a , b , and c are constants and a is not equal to 0 .