To find the vertex of the quadratic function f(x) = 1/2 x² + 3x + 2, we can use the vertex formula. For a quadratic function in the form f(x) = ax² + bx + c, the x-coordinate of the vertex can be found using the formula:
x = -b/(2a)
In this function, the coefficients are:
- a = 1/2
- b = 3
- c = 2
Plugging in the values of a and b into the vertex formula gives:
x = -3/(2 * (1/2)) = -3/1 = -3
Now that we have the x-coordinate of the vertex, we can find the corresponding y-coordinate by substituting x = -3 back into the function:
f(-3) = (1/2)(-3)² + 3(-3) + 2
This simplifies to:
f(-3) = (1/2)(9) – 9 + 2 = 4.5 – 9 + 2 = -2.5
Thus, the vertex of the function is at the point:
(-3, -2.5)
In conclusion, the vertex of the function f(x) = 1/2 x² + 3x + 2 is (-3, -2.5).