Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x - 4 = ( y - 5 ) ^ { 2 }$$
A) $y = \sqrt { x - 4 } + 5$ and $y = 5 - \sqrt { x + 4 }$
B) $y = \sqrt { x + 21 }$ and $y = - \sqrt { x - 29 }$
C) $y = \sqrt { x - 4 } + 5$ and $y = 5 - \sqrt { x - 4 }$
D) $y = \sqrt { x - 4 } + 5$ and $y = - \sqrt { x + 4 } - 5$

Question

Quizplus · Accepted Answer

To graph the given horizontal parabola, we need to solve for $y$ in terms of $x$. Starting with $x - 4 = (y - 5)^2$, we take the square root of both sides to get $y - 5 = \pm\sqrt{x - 4}$. This gives us two equations: $y = \sqrt{x - 4} + 5$ and $y = 5 - \sqrt{x - 4}$, which correspond to the upper and lower halves of the parabola, respectively.

Determine the Two Equations Necessary to Graph the Horizontal Parabola x−4=(y−5)2x - 4 = ( y - 5 ) ^ { 2 }x−4=(y−5)2

Determine the Two Equations Necessary to Graph the Horizontal Parabola $x - 4 = ( y - 5 ) ^ { 2 }$