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; \(y = \sqrt { 3 } x \pm \sqrt { - 12 \sqrt { 3 } x + 189 }\)

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Definitions:

Effective Interest Method

A method of calculating the amortized cost of a bond or loan based on periodic cash flows and interest expense adjustments.

Interest Expense

The cost incurred by an entity for borrowed funds.

Premium on Bonds Payable

The amount by which the selling price of a bond exceeds its principal (face value), often resulting from interest rates lower than the bond's coupon rate.

Par Value

The nominal value of a bond or stock as declared by the issuer.