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# What is the vertex of the function f(x) =1/2 x^{2} + 3x + 3/2 ?

**Solution:**

The given function is the equation of the parabola of the general form of equation f(x) = ax^{2} + bx + c and its graph is shown below:

The vertex of the equation of the form f(x) = ax^{2} + bx + c is given by the formula:

-b/2a

For the given equation 1/2 x^{2} + 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 x^{2} + 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 x^{2} + 3x + 3/2 ?

**Summary:**

The vertex of the function f(x) =1/2 x^{2} + 3x + 3/2 is given by the coordinates (-3, -3)

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