# The vertex form of the equation of a parabola is x = (y - 3)^2 + 41, what is the standard form of the equation?

May 3, 2017

$y = \pm \sqrt{x - 41} + 3$

#### Explanation:

We need to solve for $y$. Once we've done that, we can manipulate the rest of the problem (if we need to) to change it tnto standard form:

$x = {\left(y - 3\right)}^{2} + 41$

subtract $41$ on both sides

$x - 41 = {\left(y - 3\right)}^{2}$

take the square root of both sides

$\textcolor{red}{\pm} \sqrt{x - 41} = y - 3$

add $3$ to both sides

$y = \pm \sqrt{x - 41} + 3$ or $y = 3 \pm \sqrt{x - 41}$

The standard form of Square Root functions is $y = \pm \sqrt{x} + h$, so our final answer should be $y = \pm \sqrt{x - 41} + 3$