When we want to find the roots of a one-variable function, we look for where its graph intersects the x-axis. In this case, the graph intersects the x-axis at
The vertex of a parabola is the highest or lowest point on it, depending on whether the leading coefficient of the quadratic function is negative or positive. In this case, we see that the lowest point is
For the y-intercept, just look for where the graph intersects the y-axis; in this case, that point is
Using this information, the vertex-form equation of the parabola is so the factors are two copies of
In this case, the value of
in the equation
was conveniently 1; if that's not the case, you'll want to plug in
to solve for the value of a that gives the correct y-intercept.
Does that help clear things up?
