Yours Truly answers: The Factored Form is of the form f(x) = a(x – x₁)(x – x₂). The key to this type is NOT to expand what is already nicely factored.

Say, we want to graph:

There are four things that we should immediately notice:

1) If we mentally expand the right-hand side (RHS), we see that the coefficient of the leading term  x²  would be 1, which is positive. So, the parabola must be open UP.

2) We always set RHS=0 to seek x-intercepts. As we do just that in this problem, we get

3) Recall that the x-coordinate of the vertex must be the midpoint between the x-intercepts.

4) The moment we know the x-coordinate, we can compute the y-coordinate of the vertex.

5) We always compute  f(0)  to obtain the y-intercept. So,

1)—5) provide all we need to accurately graph the parabola: