What are quadratic functions and how do they work?

What are quadratic functions and how do they work?

Quadratic functions are polynomial functions of degree two, typically in the form of f(x) = ax² + bx + c. They graph as parabolas.

Can you explain the components of the quadratic formula?

Sure! The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). Here, a, b, and c are coefficients from the quadratic equation.

What does the discriminant tell us about the roots?

The discriminant, b² - 4ac, indicates the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

How can I find the vertex of a quadratic function?

The vertex can be found using the formula (-b/(2a), f(-b/(2a))). This gives you the x-coordinate and you can substitute it back to find the y-coordinate.

Can you give me an example of a quadratic function?

Sure! An example is f(x) = 2x² - 4x + 1. This function opens upwards and has a vertex that can be calculated using the methods we discussed.