Pls help me please please

1. what is the phythaforean theorem? 2.what do we use it for? 1.what is the distance formula ? 2.what do we use it for?

If you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?

To find the extreme values of a function f(x.y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x,y)=xy