You may want to review solving quadratic equations first.

Quadratic functions are like *y* = *x*^{2} +
6*x* − 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 *x*^{2} + 6*x* − 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*
= *ax*^{2} + *bx* + *c*, its vertex is
at *x* = −*b* / (2*a*), so, in our example,
it's *x* = −3.