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).