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

Expert Answers
justaguide eNotes educator| Certified Educator

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.