g(x)=sqrt(x-1)

Question

I need the answer as quadratic function

Answer 1

Roxann,

 

A quadratic function has the form  g(x) = ax² + bx + c,   where a, b & c are constant coefficients

 

So starting with your function g(x) = (x - 1)^1/2  , where the 1/2 power represents the square root

Then  g²(x) = g(x)g(x) = (x -1)  and the square root goes away by squaring both sides of this equality

and g⁴(x) = g²(x)g²(x) - (x - 1)² = x² - 2x +1

 

Therefore, g4(x) is a quadratic equation with a=1 , b=-2, and c=1

 

Also note that g²(x) = x - 1 which is actually linear but could be thought of as a quadratic with a=0, b=1 and c=-1.

But usually the term quadratic is used whenever an ax² term is non-zero or present.