Let \( g(x)=-x^{2}+6 x+4 \). Find and simplify \( g\left(\frac{1}{2}\right) \). The value of the function is \( \square \). (Type an integer or a fraction.)

To find \( g\left(\frac{1}{2}\right) \), we will substitute \( \frac{1}{2} \) into the function \( g(x) = -x^2 + 6x + 4 \). First, calculate \( g\left(\frac{1}{2}\right) \): \[ g\left(\frac{1}{2}\right) = -\left(\frac{1}{2}\right)^2 + 6\left(\frac{1}{2}\right) + 4 \] Calculating each term: 1. \( -\left(\frac{1}{2}\right)^2 = -\frac{1}{4} \) 2. \( 6\left(\frac{1}{2}\right) = 3 \) 3. The constant term is \( 4 \) Now, combine these results: \[ g\left(\frac{1}{2}\right) = -\frac{1}{4} + 3 + 4 \] Convert \( 3 \) and \( 4 \) into fractions with a common denominator of \( 4 \): - \( 3 = \frac{12}{4} \) - \( 4 = \frac{16}{4} \) Now, add them together: \[ g\left(\frac{1}{2}\right) = -\frac{1}{4} + \frac{12}{4} + \frac{16}{4} = \frac{-1 + 12 + 16}{4} = \frac{27}{4} \] Thus, the value of the function is: \[ \boxed{\frac{27}{4}} \]