#1**+3 **

This is one way of doing it.

We want to get the function into vertex form.

y = x^{2} - 4x + 2 Subtract 2 from both sides.

y - 2 = x^{2} - 4x Add (-4/2)^{2} , or 4, to both sides.

y - 2 + 4 = x^{2} - 4x + 4 Now that the right hand side is a perfect square trinomial, factor it.

y + 2 = (x - 2)(x - 2)

y + 2 = (x - 2)^{2} Subtract 2 from both sides.

y = (x - 2)^{2} - 2

When the equation is in this form, we can see that this is the graph of y = x^{2} shifted to the *right* 2 units and shifted *down* 2 units. The vertex is at (2, -2). So plot the first point at (2, -2) and go up just like a basic parabola from there. :)

hectictar
May 1, 2017