Question

Which of the following identifies the quadratic function that is related to the square root function m(x)=x−2−−−−√+4
?(1 point)
Responses

n(x)=(x−4)2+2

n left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis squared plus 2

n(x)=14x2+2

n left parenthesis x right parenthesis equals Start Fraction 1 over 4 End Fraction x squared plus 2

n(x)=4x2+2

n left parenthesis x right parenthesis equals 4 x squared plus 2

n(x)=(x+4)2−2

Answer 1

Answer: n(x) = (x − 4)^2 + 2.

Reason: Let y = sqrt(x − 2) + 4. Then y − 4 = sqrt(x − 2). Squaring gives (y − 4)^2 = x − 2, so x = (y − 4)^2 + 2. Swapping variables yields the quadratic n(x) = (x − 4)^2 + 2.