Given #y=a(x-h)^2+k#...what is the correct expression for #x#: #1.# #x=sqrt((y+2)/h)# #2.# #x=sqrt((y+2)/h)# #3.# #x=h+-sqrt((y-k)/a)# #4.# #"A simple expression for x cannot be derived."#?

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Answer 1 · 2017-01-05T22:29:22

#"The third option..........."#

We have #y=a(x-h)^2+k#

As with any equation, we can divide it, multiply it, add to it, subtract from it etc., provide we do it to BOTH SIDES:

So we want #x#, and we begin be subtracting #k# from both sides:

#y-k=a(x-h)^2+k-k#

#y-k=a(x-h)^2#

And now we divide BOTH sides by #a#:

#(y-k)/a=(x-h)^2#

And we take the square root of each side, remembering that a square can have positive or negative roots:

#sqrt((y-k)/a)=sqrt((x-h)^2)#

#sqrt((y-k)/a)=+-(x-h)#

OR #+-sqrt((y-k)/a)=(x-h)#

And (finally) #x=h+-sqrt((y-k)/a)#, as required............