Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Select three options.The domain is {x|x ≤ –2}.The range is {y|y ≤ 6}.The function is increasing over the interval (–∞ , –2).The function is decreasing over the interval (−4, ∞).The function has a positive y-intercept.

Answer:The true statements about the graph of the function are:The range of the function is {y : y ≤ 6} ⇒ 2nd The function is increasing over the interval (–∞ , –2) ⇒ 3rdThe function has a positive y-intercept ⇒ 5thStep-by-step explanation:* Lets explain how to solve the problem- The function f(x) = -x² - 4x + 2 is a quadratic function represented   graphically by a downward parabola with maximum vertex∵ The form of the quadratic function is f(x) = ax² + bx + c∵ The coordinates of the vertex of the parabola are (h , k) where    h = -b/2a and k = f(h)∵ a = -1 , b = -4∴ h = -(-4)/2(-1) = 4/-2 = -2∵ k = f(h)∴ k = -(-2)² - 4(-2) + 2 = -(4) - (-8) + 2∴ k = -4 + 8 + 2 = 6∴ The vertex of the parabola is (-2 , 6)* Look to the attached figure to find the true statements∵ The greatest value of the function is 6 ⇒ y-coordinate of the vertex∵ The range of the function is the values y-coordinates of the points   on the parabola∴ The range of the function is {y : y ≤ 6} - The domain of the function is {x : x ∈ R} or (-∞ , ∞) ∵ The value of y increasing after -∞ to the x-coordinate of the vertex∵ x-coordinate of the vertex is -2∴ The function is increasing over the interval (–∞ , –2)- The parabola intersect the y-axis at point (0 , 2)∵ The y-intercept is the intersection between the parabola and the    y-axis ∵ The parabola intersect the y-axis at point (0 , 2)∴ The y-intercept is 2∴ The function has a positive y-intercept