What is the vertex of the graph y=x^2+3x-4

The vertex of the graph is the extreme point that can be
determined in many ways.

I'll use the first derivative
method. The roots of the 1st derivative represent the critical points of the
function.

f'(x) = 2x + 3

We'll
cancel the first derivative:

2x + 3 =
0

x = -3/2

Since the leading
coefficient is positive, therefore the vertex of the graph is the minimum point of the
function.

f(-3/2) = 9/4 - 9/2 -
4

f(-3/2) =
(9-18-16)/4

f(-3/2) =
-25/4

The coordinates of the vertex are:
V(-3/2 ; -25/4).