is there another way to finding the quadratic function given three points on the parabola besides substituting the x and y values to find the...

To determine a quadratic function means to compute it's
coefficients. Indeed, the system of equations method is the most usually applied since
it is quite easy to substitute the given values of coordinates within the quadratic
resulting a linear equation with 3 variables (a,b,c-coefficients) for each given point.
To determine the solution of this system we need three points to generate three
equation, since there are 3 coefficients to find out.

But
there are many other methods, as well.

One of them is
vertex method that allows us to write the equation of parabola in "vertex
form":

`y = a(x - h)^2 +
k`

Other method is to use a math software that helps you to
find the function. For instance, you can use Excel to generate the parabola, plugging 
the given values of the points in the specified cells.