effect of changing b on graph of f(x)=ax^2+bx+c

When the value of b in the quadratic function y = ax^2 +
bx + c is changed, the graph's shape remains the same, only its position
changes.

The graph opens upwards or downwards depending on
the sign of a. The sign of b has no effect on that. The concavity of the graph is also
not affected by the value of b. There is just a shift in the position of the graph which
may be upwards, downwards, to the left or to the right. The new graph is located such
that the roots of the equation are located at the appropriate location on the
x-axis.

You can use the link provided below to enter
functions with different values of b and see the changes due to
it.

A change in b only results in a movement
of the graph with respect to the x and y axes.