You can put this solution on YOUR website!
The x-coordinate of the vertex of a parabola in the form
is given by
The y-coordinate is then
The line of symmetry passes through the vertex, so the equation is
The maximum or minimum is the value of the function at
. Whether it is a maximum or minimum depends on whether the parabola opens up or down. If it is concave up (makes a valley rather than a hill), the point is a minimum, otherwise it is a maximum. You can tell which way the parabola opens by the sign on the lead coefficient. if
, it is concave down, if
, it is concave up, and, of course, if
you don't have a parabola at all.
Let's look at your specific problem:
First thing to note is that
, so this is a concave down parabola and the vertex is a maximum.
, so the x-coordinate of the vertex is
and the equation of the line of symmetry is
The value of the function at
for your problem is
So the y-coordinate of the vertex and the maximum value of f is