Graphing and Analyzing Equations

This video tutorial teaches how to solve systems of quadratic and linear equations by graphing. It begins with an introduction to systems of equations and common graphing mistakes. The tutorial then demonstrates graphing a parabola and a line, followed by graphing a circle and a line, to find common points or intersections. The video concludes with a summary of the graphing method for solving these systems.

What is a system of equations?

• A group of two or more equations

• A single equation with two variables

• A graph with no intersections

• An equation with no solutions

What is a common mistake when graphing equations?

• Using a graphing calculator

• Sketching the wrong graph

• Using a pencil and paper

• Finding the intersection point

What does it mean if two graphs do not intersect?

• They are the same graph

• They have one solution

• They have no real number solutions

• They have multiple solutions

In the first example, what type of graph is x squared minus two x plus one?

• A line

• A parabola

• A circle

• A hyperbola

In the first example, what is the equation of the line after rearranging y + 3 = x?

• y = x + 3

• y = x - 3

• y = -x + 3

• y = -x - 3

What shape does the equation x squared plus y squared equals four represent?

• An ellipse

• A circle

• A parabola

• A line

In the second example, what is the slope of the line y = -x + 4?

• 1

• 4

• -1

• 0

What is the center of the circle represented by x squared plus y squared equals four?

• (-2, -2)

• (0, 0)

• (2, 2)

• (4, 4)

What is the radius of the circle in the second example?

• 4

• 3

• 2

• 1

What is the main takeaway from this lesson?

• Graphing is not useful for solving equations

• Graphing can help identify if systems have solutions

• Quadratic equations are easier to solve than linear equations

• Systems of equations always have solutions