i have questions about parts of the parabola standard form. I know that it is ax^2+bx+c but what does b and c represent.
a = the width of the parabola
If l a l < 1...the graph is wider than the graph y = x^2, if l a l > 1....the graph is narrower than the graph y = x^2 and if a < 0....we have an "upside" down parabola
c = the y intercept
b...when this isn't 0, it shifts the vertex of the graph off of the y axis....either left or right
Look at these graphs to get a feel for this :
Yes...without "b," all vertcal parabolas would have a vertex on the y axis....but, of course, the vertex can definitely be away from the y axis