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............

Given y=a(x-h)^2+ky=a(x-h)^2+k...what is the correct expression for xx: 1.1. x=sqrt((y+2)/h)x=sqrt((y+2)/h) 2.2. x=sqrt((y+2)/h)x=sqrt((y+2)/h) 3.3. x=h+-sqrt((y-k)/a)x=h+-sqrt((y-k)/a) 4.4. "A simple expression for x cannot be derived.""A simple expression for x cannot be derived."?