Solving Systems of Equations

This video tutorial explains how to graph nonlinear systems, specifically a quadratic and a line. It covers the process of graphing a parabola by finding its vertex and using a pattern based on the lead coefficient. The tutorial then demonstrates how to graph a line using its slope and y-intercept. Finally, it shows how to find the intersection points of the parabola and the line, which represent the solutions to the system of equations.

What is the main goal when solving a system of equations involving a parabola and a line?

• To find the vertex of the parabola

• To determine the slope of the line

• To find the points where the parabola and line intersect

• To calculate the area between the parabola and the line

What is the vertex of the parabola in the given system?

• (0, 0)

• (0, -2)

• (2, 0)

• (2, 2)

How do you determine the pattern for plotting points on a parabola?

• By using the lead coefficient and symmetry

• By using the x-intercept of the parabola

• By using the slope of the line

• By using the y-intercept of the line

What is the y-intercept of the line in the system?

• 8

• -8

• 5

• 0

How is the slope of the line used in graphing?

• To find the x-intercept

• To calculate the rise over run for plotting

• To determine the y-intercept

• To find the vertex of the parabola

Which of the following is NOT a step in graphing the line?

• Drawing the line through plotted points

• Identifying the y-intercept

• Using the slope to plot points

• Finding the vertex

At which points do the parabola and the line intersect?

• (0, -2) and (2, 2)

• (1, 1) and (2, 2)

• (2, 2) and (3, 7)

• (0, 0) and (3, 7)

What is the significance of the intersection points in the system?

• They indicate the slope of the line

• They show the symmetry of the parabola

• They are the solutions to the system of equations

• They represent the maximum points of the parabola

What method is used to solve the quadratic and linear system in this tutorial?

• Elimination

• Graphing

• Factoring

• Substitution

What is the final solution to the system of equations in this tutorial?

• The y-intercept of the line

• The intersection points

• The slope of the line

• The vertex of the parabola