(Real functions and equations) How to select points for a graph.

[Kyriakos1]

When I am given a function quadratic, square-root and inverse variation I am often uncertain as to how to select my points to graph the function. Usually I can find my vertex easily enough and y and x intercepts if any but otherwise I don't know how to select my points. Are there base points for each function? Such as (0,0), (1,1), (4,2), (8,2.8) for a function of square-root or (0,0), (1,1), (2,4), (-1,1), (-2,4) for a quadratic function.

 

[MarkFL]

If I am given a function of the form:

$$f(x)=a\sqrt{g(x)}+b$$

Then, I will find $x=x'$ such that:

$$g(x')=n^2$$ where $$n\in\mathbb{N_0}$$

Then I plot the points:

$$(x,y)=(x',an+b)$$

If I am given a function of the form:

$$f(x)=a(x-h)^2+k$$

I let $$x=h+n$$ where $$n\in\mathbb{N_0}$$, and then for each point, reflect it across the axis of symmetry. You will get the set of points:

$$(x,y)=(h\pm n,an^2+k)$$

 

[Kyriakos1]

I thank you for answering and I do not mean to sound ungrateful but I don't really understand your explanation. I do not understand these symbols: n ∈ N 0 x′.
Also I have learned the square root-function as f(x)=a\sqrt{b(x-h)} + k and am unsure how to use f(x)=ag(x)−−−−√+b. Perhaps you can dumb it down a notch.

 

[MarkFL]

The statement $$n\in\mathbb{N_0}$$ means that n is a natural number including zero, that is:

$$n\in\{0,1,2,3,\cdots\}$$

If you are given:

$$f(x)=a\sqrt{b(x-h)}+k$$

then set:

$$b(x-h)=n^2\implies x=\frac{n^2}{b}+h$$

which generates the points:

$$\left(\frac{n^2}{b}+h,an+k\right)$$