What is the vertex of the function f(x) = 4x2 + 3x + 3?

the vertex is at (h, k) => (-3/8, 39/16)

Step-by-step explanation:

One way of determining the vertex location is to "complete the square."

f(x) = 4x2 + 3x + 3 can be rewritten as    

f(x) = 4(x^2 + (3/4)x) + 3

We complete the square of (x^2 + (3/4)x ) as follows:

(x^2 + (3/4)x + 9/64 - 9/64)    or

       (x + 3/8)^2 - 9/64  

Now re-write f(x) = 4(x^2 + (3/4)x) + 3 (from above) as

                      f(x) = 4( (x + 3/8)^2 - 9/64 ) + 3, or

                       f(x) = 4(x + 3/8)^2 - 9/16 + 48/16, or

                       f(x) = 4(x + 3/8)^2 + 39/16

Comparing this to the standard vertex equation

                        f(x) = a(x - h)^2 + k, we see that h must be -3/8 and k must be 39/16.

Thus, the vertex is at (h, k) => (-3/8, 39/16).