Use the Discriminant to Classify the Graph; Then Use the Quadratic

question 104

Multiple Choice

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ .
$$3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } - 18 \sqrt { 3 } x + 30 y + 36 = 0$$

• A) ellipse; \(\quad y = - 15 + \sqrt { 3 } x \pm \sqrt { 12 \sqrt { 3 } x + 189 }\)
• B) ellipse; \(y = - 15 + \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }\)
• C) parabola; \(y = - 15 + \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }\)
• D) parabola; \(y = \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }\)
• E) hyperbola; \(y = \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }\)

---

Definitions:

U.S. Civil War

A devastating conflict from 1861 to 1865 between the Northern states (Union) and Southern states (Confederacy), primarily over issues of slavery and states' rights.

International Events

Occurrences of significant global importance, involving multiple countries or having worldwide impacts.

Reconstruction

The period after the Civil War in the United States when the southern states were reorganized and reintegrated into the Union from 1865 to 1877.

1877

marks the year of the end of Reconstruction in the United States, characterized by the withdrawal of federal troops from the South, and the compromise that settled the disputed 1876 presidential election.