Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$x ^ { 2 } + 2 x - 7 y + 36 = 0$$
A) $( x + 1 ) ^ { 2 } = 7 ( y - 5 )$
B) $( x - 1 ) ^ { 2 } = 7 ( y - 5 )$
C) $( x - 1 ) ^ { 2 } = - 7 ( y - 5 )$
D) $( x + 1 ) ^ { 2 } = 7 ( y + 5 )$

Question

Quizplus · Accepted Answer

To convert the given equation $x^2 + 2x - 7y + 36 = 0$ to the standard form of a parabola by completing the square, we first isolate the $x$ terms and complete the square for $x$:$$x^2 + 2x = 7y - 36$$To complete the square, we add $\left(\frac{2}{2}\right)^2 = 1$ to both sides:$$x^2 + 2x + 1 = 7y - 36 + 1$$$$x^2 + 2x + 1 = 7y - 35$$$$(x + 1)^2 = 7(y - 5)$$This matches choice A.

Convert the Equation to the Standard Form for a Parabola x2+2x−7y+36=0x ^ { 2 } + 2 x - 7 y + 36 = 0x2+2x−7y+36=0

Convert the Equation to the Standard Form for a Parabola $x ^ { 2 } + 2 x - 7 y + 36 = 0$