Question 9065
most problems with quadratics that students have stem from the fact that they do not really know what they are doing -- you just do "stuff" because you are told to without understanding.


Do you know what a quadratic equation looks like if it is plotted? Its general shape is either {{{graph(200,200,-2,2,-1,5,x^2)}}} or {{{graph(200,200,-2,2,-5,1,-x^2)}}}.


Now, just look at that shape...move it around. Move it up. Move it down. Move it left and right.


How many times will that shape cross the y-axis? Answer is JUST ONCE.
How many times will that shape cross the x-axis? Answer is: mainly twice. Sometimes never and occasionally once (if the curve just touches the x-axis).


That is your answer.


2. Axis means the x- and y-axes as per any graph you draw.


Hope this helps


jon.