Analyzing Solutions: Linear and Quadratic Systems on Graphs

This lesson covers the number of possible solutions for linear and quadratic systems by examining graphs. It begins with an introduction to systems of equations, explaining how solutions are determined by the intersection of lines. The lesson then delves into polynomial degrees, focusing on linear and quadratic equations, and their respective graph shapes. It further explores the properties of quadratic graphs, such as parabolas and ellipses, and concludes with an analysis of systems combining linear and quadratic equations, highlighting the conditions for having no solution, one solution, or two solutions.

What is a system of equations?

Describe the three possibilities for the solution of a linear system of equations.

What is the degree of a polynomial equation?

How can you predict the shape of a graph for a quadratic equation?

Explain the significance of the vertex in the context of quadratic equations.

What happens when a horizontal line is drawn below the minimum of a parabola?

What are the possible outcomes when a linear equation is graphed with a quadratic equation?