Question

How do i graph the function y^2=x*(x-4)^2. I have no idea where to begin.

Answer 1

Y^2 = X(X-4)^2.

Let X = 0:
Y^2 = 0(0-4)^2 = 0,
Y = 0.

Let X = 1:
Y^2 = 1(1-4)^2 = 9,
Y = sqrt9 = +- 3.

(0,0),(1,+-3),(2,+-3.46),(3,+-1.73),
(4,0),(5,+-2.24).

Let X = -5:
Y^2 = -5(-5-4)^2 = -405,
Y=sqrt(-405) = sqrt(405*-1) =+- 20.1i.

(-5,+-20i),(-4,+-16i),(-3,+-12.1i),
(-2,+-8.49i),(-1,+-5i).

i = imaginary = sqrt(-1).