Question 7 0.5 pts Analyze the Quadratic Function \( f(x)= \) \( -2(x+1)^{2}+5 \). Determine which value in the function determines whether the graph of this function opens facing upward or opens facing downward. -2 1 5 x

The value that determines whether the graph of the quadratic function opens upward or downward is the coefficient of the squared term, which in this case is -2. A negative coefficient indicates that the parabola opens downward, creating a "frown" shape. If it were positive, the parabola would open upward, resembling a "smile" instead! To visualize this, consider that the vertex form of a quadratic equation \(f(x) = a(x-h)^2 + k\) allows you to identify the vertex as the point \((h, k)\). Here, \(h = -1\) and \(k = 5\), making the vertex the highest point of the parabola since the leading coefficient is negative. Plotting this gives you a clear picture of the parabola’s shape!