Answer:
The vertex of the function is (-3 , -3)
Step-by-step explanation:
* Lets explain how to find the vertex of the quadratic function
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a , b , c are constant
- The vertex of the quadratic function is (h , k) , where
h = -b/2a and k = f(h)
* Lets solve the problem
∵ f(x) = one-half x² + 3x + three-halves
∴ f(x) = 1/2 x² + 3x + 3/2
∵ f(x) = ax² + bx + c
∴ a = 1/2 , b = 3 , c = 3/2
∵ The coordinates of its vertex is (h , k)
∵ h = -b/2a
∴ h = -3/2(1/2) = -3/1 = -3
∴ h = -3
∵ k = f(h)
∴ k = f(-3)
∵ f(-3) = 1/2 (-3)² + 3(-3) + 3/2 = -3
∴ k = -3
∴ The vertex of the function is (-3 , -3)
