What is the axis of symmetry in a quadratic function?

What is the axis of symmetry in a quadratic function?

The axis of symmetry in a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in the form ax² + bx + c.

Can you give me an example of how to find it?

Sure! For the quadratic function f(x) = 2x² + 4x + 1, the coefficients are a = 2 and b = 4. Using the formula x = -b/(2a), we get x = -4/(2*2) = -1. So, the axis of symmetry is the line x = -1.

What does the axis of symmetry tell us about the graph?

The axis of symmetry indicates where the parabola is symmetrical. It shows the line along which the graph can be folded to create two identical halves, and it also represents the x-coordinate of the vertex of the parabola.

Is the axis of symmetry always vertical?

Yes, in quadratic functions, the axis of symmetry is always a vertical line because the graph is a parabola that opens either upwards or downwards.