Find the Domain 3x^2+2y-26=0

Problem

3*x2+2*y−26=0

Solution

1. Identify the type of equation. This is a quadratic equation in terms of x and a linear equation in terms of y representing a parabola.

2. Solve for y to express the relation as a function of x

2*y=−3*x2+26

y=−3/2*x2+13

3. Analyze the resulting function y=ƒ(x) The expression −3/2*x2+13 is a polynomial.

4. Determine the restrictions. Polynomials are defined for all real numbers because there are no denominators that could be zero and no even roots of negative numbers.

5. State the domain in interval notation. Since there are no restrictions on x the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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