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

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Answer 1 · 2017-05-03T18:55:11

#y=+-sqrt(x-41)+3#

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=(y-3)^2+41#

subtract #41# on both sides

#x-41=(y-3)^2#

take the square root of both sides

#color(red)(+-)sqrt(x-41)=y-3#

add #3# to both sides

#y=+-sqrt(x-41)+3# or #y=3+-sqrt(x-41)#

The standard form of Square Root functions is #y=+-sqrt(x)+h#, so our final answer should be #y=+-sqrt(x-41)+3#