Which of the following equations would produce a parabola? Check all that apply.–5x2 + 4x – 7y + 14 = 0–x2 + 6x + y2 – 8 = 09x2 – 12xy + 4y2 + 4x – y + 5 = 012x + 6y – 5y2 + 14 = 020x2 + 10xy – y2 + 3x – 6y + 5 = 0

For a conic Ax² + Bxy + Cy² + Dx + Ey + F = 0, a parabola has B² − 4AC = 0, provided the equation is not degenerate. In A and D, only one variable is squared, so B² − 4AC = 0. In C, B² − 4AC = (−12)² − 4(9)(4) = 0; its squared part is (3x − 2y)², and the linear terms vary along the direction where that squared part is zero, so it is a parabola. B has a negative discriminant, and E has a positive one, so neither is a parabola.

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