Graphing and Analyzing Quadratic Functions

The video tutorial demonstrates how to use Desmos to graph a quadratic function, K(x) = (-⅓)x² - 1.2x + 5.4, and analyze its key features such as the vertex, intercepts, domain, and range. It also covers solving equations and inequalities like K(x) = 2, K(x) > 2, and K(x) <= 2 by examining the graph. The tutorial emphasizes understanding the graphical representation and using technology to simplify the process.

What is the purpose of using Desmos in this example?

• To solve linear equations

• To graph and analyze a quadratic function

• To calculate derivatives

• To find the area under a curve

What is the equation of the quadratic function being analyzed?

• K(x) = x² - 4x + 4

• K(x) = 2x² - 3x + 4

• K(x) = (-⅓)x² - 1.2x + 5.4

• K(x) = x² + 2x + 1

Which tool is used to graph the function K(x) in this example?

• Wolfram Alpha

• Microsoft Excel

• GeoGebra

• Desmos

What is the vertex of the function K(x) as identified in Desmos?

• (0, 5.4)

• (-6.209, 0)

• (-1.8, 6.48)

• (2.609, 0)

What is the y-intercept of the function K(x)?

• (-1.8, 6.48)

• (0, 5.4)

• (2.609, 0)

• (-6.209, 0)

What is the domain of the quadratic function K(x)?

• All real numbers

• x = 0

• x < 0

• x > 0

What is the range of the function K(x)?

• y > 6.48

• y < 6.48

• y ≥ 6.48

• y ≤ 6.48

What is the maximum y-value of the function K(x)?

• 2.609

• 4.86

• 6.48

• 5.4

What is the x-intercept of the function K(x) at (-6.209, 0)?

• The point where the graph crosses the y-axis

• The point where the graph crosses the x-axis

• The vertex of the parabola

• The maximum y-value

What is the x-intercept of the function K(x) at (2.609, 0)?

• The vertex of the parabola

• The point where the graph crosses the x-axis

• The point where the graph crosses the y-axis

• The maximum y-value