# Vocabulary

## Parabola

A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but which can be in any orientation in its plane.

a quadratic equation is any equation having the form where x represents an unknown, and a, b, and c are constants with a not equal to 0. If a = 0, then the equation is linear, not quadratic.

## Vertex

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes

## axis of symmetry

Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halves.

## Maximum Value

A real-valued function f defined on a domain X has a global (or absolute)maximum point at x∗ if f(x∗) ≥ f(x) for all x in X. Similarly, the function has a global (or absolute) minimum point at x∗ if f(x∗) ≤ f(x) for all x in X.

## minimum value

A real-valued function f defined on a domain X has a global (or absolute) maximum point at x∗ if f(x∗) ≥ f(x) for all x in X. Similarly, the function has a global (or absolute) minimum point at x∗ if f(x∗) ≤ f(x) for all x in X.

## Terms

In Algebra a term is either:
* a single number, or
* a variable, or
* numbers and variables multiplied together.

## First difference

A finite difference is a mathematical expression of the form f(x + b) − f(x + a). If a finite difference is divided by ba, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.

## Second difference

For a sequence defined by a quadratic formula, the second differences will be constant and equal to twice the number of n2 . Determine a formula for the general term of the sequence,

## Zeros (roots)

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function fis a member x of the domain of f such that f(x) vanishes at x; that is,

In other words, a "zero" of a function is an input value that produces an output of zero .

A root of a polynomial is a zero of the associated polynomial function. The fundamental theorem of algebrashows that any non-zero polynomial has a number of roots at most equal to its degree and that the number of roots and the degree are equal when one considers the complex roots (or more generally the roots in analgebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by

has the two roots 2 and 3, since

If the function maps real numbers to real numbers, its zeroes are the x-coordinates of the points where its graph meets the x-axis. An alternative name for such a point (x,0) in this context is an x-intercept.