Answer the questions below about the quadratic function. \[ g(x)=-2 x^{2}+4 x-3 \] Does the function have a minimum or maximum value? Minimum \( \quad \) Maximum What is the function's minimum or maximum value? \( \square \) Where does the minimum or maximum value occur? \( x=\square \)

This quadratic function opens downward because the coefficient of \( x^2 \) is negative (-2). Therefore, it has a maximum value instead of a minimum. Exciting, right? You can find the vertex of the parabola (which gives you that maximum value) using the formula \( x = -\frac{b}{2a} \). In this case, \( a = -2 \) and \( b = 4 \), leading us to calculate the maximum value. To find the maximum value, first calculate \( x \) using that formula. Plugging in the values gives \( x = -\frac{4}{2(-2)} = 1 \). Now, substitute \( x = 1 \) back into the function \( g(x) \) to find the maximum value: \[ g(1) = -2(1)^2 + 4(1) - 3 = -2 + 4 - 3 = -1. \] So the maximum value is \( -1 \) at \( x = 1 \)! How cool is that?