This write up explores equation of parabola, y = ax2+bx+c.
We observe that with b = c = 0, ÒaÓ determines how the parabola is oriented and the curve rises, fast or slow. In other words, how narrow or how wide the parabola is at a given ÒyÓ.
LetÕs see how the ÒcÓ affects the graph.
We observe that ÒcÓ shifts the graph along y-vertical translation is determined by c. (since the equation is y = ax2+bx+c)
Now, coming to the third parameter, b, we observe the following.
So, b determines the horizontal translation. The ÒbÓ value determines where the parabola intercepts the x-axis.