You can
put this solution on YOUR website!
is a quadratic function.
As such, its graph is a parabola.
Unlike linear functions, which graph as straight lines, quadratic functions are allowed to have no x-intercept.
They may approach the x-axis for a while, but then they change their mind and turn away from the x-axis, never crossing it.
For your function:
for
For any other value of x,
and
There is no x-intercept, because
for all values of x.
The graph never crosses the x-axis (the y=0 line), because
is never zero.
The function has a minimum at
with
The vertex of the parabola is at that point: point(-9,7).
Your function graphs as this:
Quadratic functions can be written in the form
or
with
,
, and
being some real numbers (and a must not be zero).
When written in that form, (h,k) is the vertex, and
tells you how curvy the curve is and which way it goes.
The larger the absolute value of
, the curvier the curve is.
If
is positive, the curve goes up from the vertex on both sides, as
gets larger and larger. It looks like a smiley mouth.
If
is negative, the curve goes down from the vertex on both sides, as
gets larger and larger. It's frowning.
Your curve is smiling at you.
