Remember that for a quadratic function of the form
we can find its vertex with formula:
where
is the x-coordinate of the vertex; then we will find the y-coordinate by replacing
in our original function.
From the question know that
and
, so lets replace those values in our vertex formula to find the x-coordinate of our vertex:
Now lets replace that value into our original function to find the y-coordinate of our vertex:
Finally, we have our vertex (6,-9)
Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.