Question

Quadratic graphs y=x squared - 4x

Answer 1

This is one way of doing it.

We want to get the function into vertex form.  

y = x2 - 4x + 2                  Subtract 2 from both sides.

y - 2 = x2 - 4x                   Add (-4/2)2 , or 4, to both sides.

y - 2 + 4 = x2 - 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 = x2 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. :)