Understanding Graphs of Equations

The video tutorial explains how to find the graphical solutions to a system of equations: x = 2 - y and y = x^2 - 4. It describes the characteristics of the parabola and the linear equation, including their y-intercepts and slopes. The tutorial then identifies the intersection points of these graphs as the solutions to the system of equations.

What is the main objective when analyzing the given system of equations?

• To rewrite the equations in standard form

• To determine the y-intercept of each equation

• To find the slope of each equation

• To identify the graphs and their intersection points

What shape does the graph of y = x^2 - 4 take?

• A downward opening parabola

• A circle

• An upward opening parabola

• A straight line

What is the y-intercept of the parabola y = x^2 - 4?

• 0

• 4

• -4

• 2

How can the equation x = 2 - y be rewritten in slope-intercept form?

• y = 2x - 1

• y = 2 - x

• y = x + 2

• y = -x + 2

What is the slope of the line represented by the equation x = 2 - y?

• 2

• 0

• -1

• 1

What do the intersection points of the graphs represent?

• The maximum values of the functions

• The solutions to the system of equations

• The x-intercepts of the graphs

• The points where the graphs are parallel

Which color represents the solutions to the system of equations in the video?

• Red

• Green

• Yellow

• Blue