Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$x - 4 = ( y - 7 ) ^ { 2 }$
A) $y = \sqrt { x - 4 } + 7$ and $y = - \sqrt { x + 4 } - 7$
B) $y = \sqrt { x + 45 }$ and $y = - \sqrt { x - 53 }$
C) $y = \sqrt { x - 4 } + 7$ and $y = 7 - \sqrt { x + 4 }$
D) $y = \sqrt { x - 4 } + 7$ and $y = 7 - \sqrt { x - 4 }$

Question

Quizplus · Accepted Answer

To graph a horizontal parabola, we need to solve for $y$. The given equation is $x - 4 = (y - 7)^2$. Taking the square root of both sides gives two equations: $y - 7 = \sqrt{x - 4}$ and $y - 7 = -\sqrt{x - 4}$. Solving each for $y$ gives $y = \sqrt{x - 4} + 7$ and $y = 7 - \sqrt{x - 4}$, which matches option D.

Determine the Two Equations Necessary to Graph the Horizontal Parabola x−4=(y−7)2x - 4 = ( y - 7 ) ^ { 2 }x−4=(y−7)2

Determine the Two Equations Necessary to Graph the Horizontal Parabola $x - 4 = ( y - 7 ) ^ { 2 }$