The formula is in a quadratic formula shape: [tex]y = ax^2+bx+c[/tex]
The function is negative since the value 'a' the coefficient of x^2 is negative meaning that the quadratic function is facing downards. If you don't get this explanation, take a look at the diagram I uploaded.
That means the highest point of the graph is its vertex.
But we must find where the vertex is at or the 't' value.
't' value at which vertex is = [tex]-\frac{b}{2a} =-\frac{16}{2*(-16)} =\frac{1}{2}[/tex]
Now plug this 't' value into h(t) to find the maximum height, and we will get 36 feet.
Hope that helps!
