Graphing Inequalities and Parabolas

This video tutorial covers solving systems of inequalities by graphing, focusing on quadratic inequalities. It reviews graphing techniques, explains how to determine vertices, plot points, and decide on solid or broken lines. The video demonstrates shading regions to find solutions and concludes with identifying the intersection of shaded areas as the solution to the system.

What is the main topic of this video?

• Calculating derivatives

• Graphing systems of inequalities

• Solving linear equations

• Finding integrals

What type of graph is used for inequalities with 'greater than or equal to'?

• Dashed line

• Solid line

• Dotted line

• No line

What type of graph is used for inequalities with 'less than'?

• Dotted line

• Solid line

• Dashed line

• No line

What is the first step in solving the first example of quadratic inequalities?

• Determining the vertex

• Finding the axis of symmetry

• Identifying the y-intercept

• Calculating the slope

How do you determine the vertex of a parabola in this context?

• Switch and keep method

• Add and subtract method

• Multiply and divide method

• None of the above

What equation is used to find additional points for the first parabola?

• y = -x^2

• y = -2x

• y = x^2

• y = 2x

What is the significance of the negative sign in the equation y = -x^2?

• It indicates the parabola is horizontal

• It has no significance

• It indicates the parabola opens downwards

• It indicates the parabola opens upwards

Where do you shade for a 'less than' inequality?

• To the right of the vertex

• To the left of the vertex

• Below the vertex

• Above the vertex

What is the vertex of the second parabola?

• (1, 3)

• (-2, -8)

• (-1, -3)

• (2, 8)

What equation is used to find additional points for the second parabola?

• y = x^2

• y = -2x

• y = -x^2

• y = 2x