7. Which of the given characteristics describe parabolas that open up? Explain your reasoning. A. focus: (0, 3) directrix: y = -3 B. focus: (0, -5) directrix: y = 5 C. focus: (0, -10) directrix: y = 10

↑ OT 15

Find im t ant seczt

Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y=xlnx-x+(Ink) x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x - x x ln x-x+(In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.