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

question 90

Multiple Choice

Use the discriminant to classify the graph; then use the quadratic formula to solve for $y$ .
$$3 x ^ { 2 } - 2 \sqrt { 3 } x y + y ^ { 2 } + 10 \sqrt { 3 } x - 6 y - 24 = 0$$

• A) ellipse; \(y = 3 + \sqrt { 3 } x \pm \sqrt { 4 \sqrt { 3 } x + 33 }\)
• B) ellipse; \(y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• C) parabola; \(y = 3 + \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• D) parabola; \(y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)
• E) hyperbola; \(y = \sqrt { 3 } x \pm \sqrt { - 4 \sqrt { 3 } x + 33 }\)

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Definitions:

Cancer

A broad term for diseases characterized by the uncontrolled growth and spread of abnormal cells in the body.

Correlation Coefficient

A numeric metric showing how much two variables move in relation to each other.

Alcohol Consumption

The drinking of alcoholic beverages and the societal, health, and personal impacts it may have.

Correlation

A statistical measure that expresses the extent to which two variables change together, but does not imply causation.