For a thorough review of quadratic functions, including going from standard to vertex form,
read
Quadratic Functions and the
Completing the Square Technique
.
SUMMARY: PROPERTIES OF QUADRATIC FUNCTIONS 

$y = ax^2 + bx + c$ (standard form) 
$y = a(xh)^2 + k$ (vertex form) 
COMMENTS  
GRAPH 
Every quadratic function graphs as a
parabola,
which has beautiful and important reflecting properties. If you want to know the focus and directrix of $\,y = a(xh)^2 + k\,$, read Equations of Simple Parabolas. 
For $\,a > 0\,$,
$$
\cssId{s22}{\underbrace{a(xh)^2}_{\ge 0} + k \overset{\text{always!}}{\ge} k}
$$
Thus, $\,k\,$ is a
global minimum value.
For $\,a < 0\,$, $$ \cssId{s25}{\underbrace{a(xh)^2}_{\le 0} + k \overset{\text{always!}}{\le} k} $$ Thus, $\,k\,$ is a global maximum value. 

VERTEX (turning point) 
(let $\,f(x) = ax^2 + bx + c\,$) $\displaystyle\,\left(\frac{b}{2a}\ ,\ f\bigl(\frac{b}{2a}\bigr)\right)$ This is sometimes called the vertex formula, and is worth memorizing. It can be derived by completing the square; or, it's really easy with a bit of calculus! 
$(h,k)$ Note how easy it is to get the vertex from this form; hence the name ‘vertex form’ is appropriate. 
there is a horizontal tangent line at the vertex 

$\,y\,$intercept  when $\,x = 0\,$, $$\cssId{s39}{y = a\cdot 0^2 + b\cdot 0 + c = c}$$  when $\,x = 0\,$, $$\cssId{s41}{y = a(0  h)^2 + k = ah^2 + k}$$  to find where a graph crosses the $\,y\,$axis, set $\,x = 0\,$ and solve for $\,y$  
$\,x\,$intercept(s) 
use the
Quadratic Formula, as needed: $ax^2 + bx + c = 0$ is equivalent to $\displaystyle x = \frac{b\pm\sqrt{b^2  4ac}}{2a}$

easiest: isolate the squared expression; correctly ‘undo’ the square EXAMPLE: $$ \begin{gather} \cssId{s66}{0 = 2(x1)^2 5}\cr\cr \cssId{s67}{5 = 2(x1)^2}\cr\cr \cssId{s68}{\frac 52 = (x1)^2}\cr\cr \cssId{s69}{x1 = \pm\sqrt{\frac{5}{2}}} \cr\cr \cssId{s70}{x = 1\pm\sqrt{\frac{5}{2}}} \end{gather} $$ Need help with the last couple steps? Study: Solving Simple Equations Involving Perfect Squares Solving More Complicated Equations Involving Perfect Squares 
to find where a graph crosses the $\,x\,$axis, set $\,y = 0\,$ and solve for $\,x$ 
Use the following
Wolfram Alpha widgets
to graph and compute properties of quadratic functions.
After pressing ‘Submit’ be sure to scroll down to see the graphs!
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
