Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$x ^ { 2 } - 4 x - 3 y - 5 = 0$$
A) $( x - 2 ) ^ { 2 } = 3 ( y + 3 )$
B) $( x + 2 ) ^ { 2 } = 3 ( y + 3 )$
C) $( x + 2 ) ^ { 2 } = - 3 ( y + 3 )$
D) $( x - 2 ) ^ { 2 } = 3 ( y - 3 )$

Question

Quizplus · Accepted Answer

To convert the given equation $x^2 - 4x - 3y - 5 = 0$ to the standard form of a parabola by completing the square, we first isolate the $x$ terms and complete the square for $x$. Rearrange the equation to focus on the $x$ terms: $x^2 - 4x = 3y + 5$. To complete the square, add $(\frac{-4}{2})^2 = 4$ to both sides, resulting in $x^2 - 4x + 4 = 3y + 5 + 4$. This simplifies to $(x - 2)^2 = 3(y + 3)$, which matches choice A.

Convert the Equation to the Standard Form for a Parabola x2−4x−3y−5=0x ^ { 2 } - 4 x - 3 y - 5 = 0x2−4x−3y−5=0

Convert the Equation to the Standard Form for a Parabola $x ^ { 2 } - 4 x - 3 y - 5 = 0$