When we solved our equation x ^ 2 - 4x + 4 we ended up with x = 2 We call this an example of a "repeated" or "double" root. Whenever we use the quadratic formula, if we have sqrt(0) we will end up with two repeated answers, which ultimately means we have only ONE solution. Graphically, the parabola will appear to "bounce" off of the x-axis at the exact location of our ONE intercept .
Correct, when we have a repeated or double root, it means that the quadratic equation intersects the x-axis at the same point twice. This can also be seen graphically as the parabola just touching the x-axis at that point and bouncing off it. In terms of solutions, having a repeated root means that we have only one solution for the equation.
