Question

What does b do in y=ax^2+bx+c. How can b being positive or negative affect a graph?

Answer 1

The positions of the vertex and the axis of symmetry change.

Explanation:

Let’s examine three parabolas in which a and c remain constant and only b changes.

(1) y = x² - 2x + 1

(2) y = x² + 1

(3) y = x² + 2x + 1

In the image below,

Equation (1) is the black parabola, Equation (2) is green, and Equation (3) is red.

When b is more negative, the vertex moves down, and the axis of symmetry moves to the right.

When b is more positive, the vertex moves down, and the axis of symmetry moves to the left.