Write an equation of a radical (square root symbol) that has the starting point (vertex) of (5, -2).

Answer 1

The basic radical function is:

f(x) = √x

f(x) starts at the point (0,0). You want to start at (5, -2) so you want to shift right 5 and down 2. The transformations are:

g(x) = a·√(b(x-c)) + d where:

1. a = vertical dilation
2. b = horizontal dilation
3. c = horizontal shift = 5
4. vertical shift = -2

So you want:

g(x) = a√(b(x-5)) - 2

Since the problem only gives you one point, you can use any value of a and b that you want except 0; they will all start at (5,-2). The simplest is to pick a = b = 1:

g(x) = √(x-5) - 2