Understanding quadratic function - beginner calculus Drawing tangent line to $2x^2 + 2x + 4$ at $x = 3$ : 

http://www.wolframalpha.com/widgets/view.jsp?id=5c1ac7fe2da56ef0295f7fd796371a56
Taken from http://www-math.mit.edu/~djk/calculus_beginners/chapter04/section02.html : 

If you look at a quadratic function f at some particular argument,
  call it z, and very close to z, then f will look like a straight line.
  The line f resembles at argument z is called the tangent line to f at
  argument z, and the slope of this tangent line to f at z is called the
  derivative of f at argument z.

Is the z argument in this case the value 3 ?
Is following statement correct : 

If you look at a quadratic function $2x^2 + 2x + 4$ at argument $x=3$,
  $2x^2 + 2x + 4$ will look like a straight line very close to argument
  x=3.
  The line $2x^2 + 2x + 4$ resembles at argument $x=3$ is called the
  tangent line to   $2x^2 + 2x + 4$ at argument $x=3$ and the slope of this
  tangent line to $2x^2 + 2x + 4$ at $x=3$ is called the derivative of 
  $2x^2 + 2x + 4$ at argument $x=3$.

 A: yes z=3
The word "very close" means if you zoom in into the graph of f, then f will looks like a straight line. The straight line looks like the tangent line at any argument(example x=3).
A: Answering your question: "Is the following correct....":
The way the sentence is written is confusing.
In short (and without being strict mathematically...): 


*

*The derivative of a function of degree $2$ (Quadratic equation) is a function of degree one (a straight line) and can be refereed to as f'(x).

*The derivative of a function $f(x)$ at any point $(s, f(s))$ represents the general equation of the slope. The value of the derivative at a point $(s, f'(s))$ is the slope at the point (s, f(s)). Notice careful y the difference between f and f' symbols. f represents the function, whereas f' represents the derivative.
The above is illustrated in hundreds of sites and books under the concept of derivatives and is fundamental to understanding Calculus.
If you have an issue I could explain further and give you references, for example:Meaning of the Derivative.
