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?

• A set of equations with the same variables

• A set of equations with different variables

• A single equation with multiple variables

• An equation with no variables

What is the degree of a linear equation?

• One

• Three

• Two

• Zero

How does a quadratic graph differ from a linear graph?

• It is a straight line

• It is a curve

• It has no variables

• It is a point

What shape does the graph of y = x^2 form?

• A parabola

• An ellipse

• A circle

• A straight line

In a quadratic graph, how many inputs can a single output have?

• Two

• Three

• Four

• One

What happens when a line intersects a parabola at two points?

• There is no solution

• There is one solution

• There are two solutions

• There are infinite solutions

How many solutions can a linear and quadratic system have?

• None, one, or two

• Only one

• Only two

• Infinite