Two quadratic functions are represented below.

in two or more complete sentences, explain how you can determine the maximum value of the quadratic functions, f(x) and g(x).
which function has the greater maximum value, f(x) or g(x)?

To determine the maximum value of a quadratic function opening downwards, we are going to find the vertex; then the y-value of the vertex will be our maximum.
To find the vertex (h,k) (where h=x-coordinate and k=y-coordinate) of a quadratic function of the form  we'll use the vertex formula: , and then we are going to replace that value in our original function to find k.

So, in our function ,  and . 
Lets replace those values in our vertex formula:




Now that we know the x-coordinate of our vertex, lets replace it in the original function, to get the y-coordinate:




We just prove that the vertex of  is (2,1), and for the graph we can tell that the vertex of  is (-2,4). The only thing left is compare their y-coordinates to determine which one has the greater maximum value. Since 4>1, we can conclude that  has the greater maximum.