Understanding Quadratic Functions with No Zeros or Real Roots

This lesson explores the limitations of using zeros to graph quadratic functions, focusing on functions with no real roots. It explains how parabolas, the graphs of second-degree polynomials, behave based on their factors and coefficients. An example involving a patio project illustrates a polynomial with no real roots. The lesson also covers the appearance of graphs for such polynomials and concludes with a mention of other techniques for handling non-factorable quadratics.

What does it mean for a quadratic function to have no real roots?

How can a quadratic function still cross the x-axis even if it is not easily factorable?