



 
For the parabola $y = a x^2 + b x + c$ "a" is best thought of as determining the curvature (inverse to width) "b" determines the slope at x=0. If this is nonzero it pushes the vertex If "c" is zero then the yintercept is at y=0 (and there is an xintercept at x=0.) In general, the yintercept is at y=c; so c slides the parabola up or down. Other important quantities are $\large \frac{b}{2a}$ (the x coordinate of the vertex and the line of symmetry), $c\large \frac{b^2}{4a}$ (y coordinate of the vertex), Good Hunting!  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 