Find the maximum or minimum value of \( f(x)=-3 x^{2}+36 x-8 \) The Select an answer \( \theta \) is

To find the maximum or minimum value of the quadratic function \( f(x) = -3x^2 + 36x - 8 \), we can use the vertex formula. The x-coordinate of the vertex, which gives the location of the maximum or minimum, is found using \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 36 \). Calculating this gives: \[ x = -\frac{36}{2 \cdot -3} = \frac{36}{6} = 6. \] Now, plug this value back into the function to find \( f(6) \): \[ f(6) = -3(6)^2 + 36(6) - 8 = -3(36) + 216 - 8 = -108 + 216 - 8 = 100. \] Since the leading coefficient is negative, the function opens downwards, meaning this point is a maximum. Thus, the maximum value of \( f(x) \) is \( 100 \). The answer for \( \theta \) is \( 100 \).