Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$x + 3 = ( y + 6 ) ^ { 2 }$
A) $y = \sqrt { x - 3 }$ and $y = - \sqrt { x - 3 }$
B) $y = \sqrt { x + 3 } - 6$ and $y = - \sqrt { x + 3 } - 6$
C) $y = \sqrt { x + 9 }$ and $y = - \sqrt { x + 9 }$
D) $y = \sqrt { x + 3 } - 6$ and $y = - \sqrt { x + 3 } + 6$

Question

Quizplus · Accepted Answer

To graph the given horizontal parabola $x + 3 = (y + 6)^2$ on a calculator, we need to solve for $y$ in terms of $x$. Taking the square root of both sides gives two equations: $y + 6 = \sqrt{x + 3}$ and $y + 6 = -\sqrt{x + 3}$. Solving these for $y$ yields $y = \sqrt{x + 3} - 6$ and $y = -\sqrt{x + 3} - 6$, which are the equations in choice B.

Determine the Two Equations Necessary to Graph the Horizontal Parabola x+3=(y+6)2x + 3 = ( y + 6 ) ^ { 2 }x+3=(y+6)2

Determine the Two Equations Necessary to Graph the Horizontal Parabola $x + 3 = ( y + 6 ) ^ { 2 }$