Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$y ^ { 2 } + 6 y - 5 x + 14 = 0$$
A) $( y + 3 ) ^ { 2 } = 5 ( x - 1 )$
B) $( y - 3 ) ^ { 2 } = 5 ( x - 1 )$
C) $( y - 3 ) ^ { 2 } = - 5 ( x - 1 )$
D) $( y + 3 ) ^ { 2 } = 5 ( x + 1 )$

Question

Quizplus · Accepted Answer

To convert the given equation $y^2 + 6y - 5x + 14 = 0$ to the standard form of a parabola by completing the square, we first isolate the $y$ terms and move the $x$ term to the other side:$$y^2 + 6y = 5x - 14$$To complete the square, we take the coefficient of $y$, which is $6$, divide it by $2$, and square it, giving us $(6/2)^2 = 3^2 = 9$. We add and subtract $9$ on the left side to maintain equality:$$y^2 + 6y + 9 = 5x - 14 + 9$$Simplifying, we get:$$(y + 3)^2 = 5x - 5$$Rearranging the $x$ term to isolate $x$, we get:$$(y + 3)^2 = 5(x - 1)$$This matches choice A: $(y + 3)^2 = 5(x - 1)$.

Convert the Equation to the Standard Form for a Parabola y2+6y−5x+14=0y ^ { 2 } + 6 y - 5 x + 14 = 0y2+6y−5x+14=0

Convert the Equation to the Standard Form for a Parabola $y ^ { 2 } + 6 y - 5 x + 14 = 0$