You may want to review solving quadratic equations first.
Quadratic functions are like y = x2 + 6x − 1. Like all functions, they have a y-intercept, which we get by plugging in 0 for x. In this case, it's −1. You can also find x-intercepts by setting y = 0 and solving for x. So we have to solve the equation x2 + 6x − 1 = 0. The Quadratic Formula gives us two solutions, −3 + √10 and −3 − √10, so these are the x-intercepts. (This is different from linear functions, which can only have one x-intercept; quadratic functions can have none, one or two. They always have exactly one y-intercept, though.)
Another thing that quadratic functions have is a vertex. The vertex is the value of x where y is biggest or smallest. (Your teacher will probably be able to draw some pictures for you which will make this much clearer.) In any event, if your quadratic function is y = ax2 + bx + c, its vertex is at x = −b / (2a), so, in our example, it's x = −3.