Answer:
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).
