Rewrite the equation in standard form. Determine whether the parabola is horizontal or vertical, the direction it opens,
and the vertex.
-$$x = y ^ { 2 } + 14 y + 44$$
A) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the right, vertex $( - 5 , - 7 )$
B) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the right, vertex $( - 7 , - 5 )$
C) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the left, vertex $( - 5 , - 7 )$
D) $x = ( y + 5 ) ^ { 2 } - 7$
horizontal, opens to the left, vertex $( - 7 , - 5 )$

Question

Quizplus · Accepted Answer

The equation can be rewritten in the form $x = (y + 7)^2 - 5$ by completing the square. Since $x$ is isolated on one side, the parabola is horizontal. It opens to the right because the coefficient of $y^2$ is positive. The vertex is at $(-5, -7)$, obtained by setting the inside of the square to zero and solving for $x$ and $y$.

Rewrite the Equation in Standard Form x=y2+14y+44x = y ^ { 2 } + 14 y + 44x=y2+14y+44

Rewrite the Equation in Standard Form $x = y ^ { 2 } + 14 y + 44$