Use the Discriminant to Determine If the Graph of the Equation

question 90

Essay

Use the discriminant to determine if the graph of the equation $\frac { 3 } { 4 } x ^ { 2 } + \frac { \sqrt { 3 } } { 2 } x y + \frac { 1 } { 4 } y ^ { 2 } + 4 x - 4 \sqrt { 3 } y = 0$ is a parabola, an ellipse or a hyperbola, and then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.

Understand the social and economic challenges faced by American cities in the late 19th and early 20th centuries, including housing, sanitation, and urban poverty.

Comprehend the impact of immigration on American society and the economy between 1880 and 1920.

Analyze the objectives, means, and effectiveness of civic reformers.

Understand the causes and effects of major labor conflicts during this period and the reactions from the government and the public.

---

Definitions:

Frederick W. Taylor

An American engineer and management consultant who is known as the father of scientific management, focusing on efficiency and labor productivity.

Piece Rates

A payment method in which a worker is paid a fixed rate for each unit produced or action performed, regardless of time.

Unity of Direction

A management principle suggesting that all parts of an organization should be aligned and moving towards common objectives.

Home Building Company

A business organization that specializes in constructing residential homes for clients.