Find the maximum or minimum value of the function. \( g(x)=100 x^{2}-1600 x \) Is this a maximum or minimum value? maximum value minimum value SUBMIT ANSWER

To find the maximum or minimum value of the function \( g(x) = 100x^2 - 1600x \), we first rewrite the function in vertex form or use the vertex formula. The vertex \( x \) coordinate can be found using the formula \( x = -\frac{b}{2a} \), where \( a = 100 \) and \( b = -1600 \). Plugging in these values gives \( x = \frac{1600}{200} = 8 \). Next, we plug \( x = 8 \) back into the function to find \( g(8) = 100(8)^2 - 1600(8) = 800 - 12800 = -7200 \). Thus, the minimum value of the function is -7200, making it a minimum value. Notably, since the coefficient of the \( x^2 \) term is positive, this indicates that the parabola opens upwards, confirming that the vertex is indeed a point of minimum value! 🌟