The formula for the area of a square, where  
is the length of each side is 



Substitute 18 for A



Take square roots of both sides





So each side is 

We draw the square:



Let's draw a diagonal:



Use the Pythagorean theorem to find the length 
of the diagonal:




Taking square roots:


Now since the diagonal is 6, let's tilt the square
45° and put the diagonal along the y-axis with a 
corner at the origin, like this: 



We draw the other diagonal:



Since the vertical diagonal is 6 units,
so is the horizontal diagonal, so
the two vertices at the end of the
horizontal diagonal are 
and  

We put the coordinates at these corners:



Now we can roughly sketch in the parabola
we are looking for:

We put the coordinates at these corners:



Since the parabola has the form ,
and goes through , 
we substitute  and 






  

The value of  is therefore  and
the equation of the parabola is

  

Edwin