What is the vertex of the function f(x) =1/2 x² + 3x + 3/2 ? 

Solution:

The given function is the equation of the parabola of the general form of equation f(x) = ax² + bx + c and its graph is shown below:

The vertex of the equation of the form f(x) = ax² + bx + c is given by the formula:

-b/2a

For the given equation 1/2 x² + 3x + 3/2:

a = 1/2 ;  b = 3 and c = 3/2 

The x coordinate of the vertex is given by :

x =  -3/(2)(1/2) = -3 

The value of y coordinate is therefore given by substituting the value of x in the given quadratic equation 1/2 x² + 3x + 3/2:

y = (1/2)*(-3)²  + 3(-3) + 3/2

y = (1/2)(9) - 9 + 3/2

   = 4.5 - 9 - 1.5

   = -3

The coordinates of the vertex of the given equation is given by (-3, -3) which is also revealed by the given graph.

What is the vertex of the function f(x) =1/2 x² + 3x + 3/2 ?

Summary:
 The vertex of the function f(x) =1/2 x² + 3x + 3/2 is given by the coordinates (-3, -3)