Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Select three options.

To determine which statements about the graph of the function f(x) = –x^2 – 4x + 2 are true, we need to analyze the function's properties. Here are common properties we can derive:

1. The graph is a parabola since it's a quadratic function (the highest power of x is 2). 2. The coefficient of x^2 is negative (-1), indicating that the parabola opens downwards. 3. To find the vertex of the parabola, we can use the vertex formula, x = -b/2a. In this case, a = -1 and b = -4, so x = -(-4)/(2 * -1) = 4/-2 = -2. 4. To find the y-coordinate of the vertex, substitute x = -2 back into the equation: f(-2) = -(-2)^2 - 4(-2) + 2 = -4 + 8 + 2 = 6. So the vertex is at (-2, 6). 5. The y-intercept occurs when x = 0. So f(0) = –(0)^2 – 4(0) + 2 = 2. The y-intercept is (0,2). 6. Since the parabola opens downwards and the vertex is the maximum point, the y-value of the vertex, 6, is the maximum value of the function.

Therefore, based on the analysis above:

- The parabola has a maximum point (which is at the vertex). - The y-intercept of the graph is 2. - The vertex is at the point (-2, 6).

Only three of these statements should be chosen, as those are the inherent characteristics of the graph of the function given.