Answer:
steps below
Step-by-step explanation:
From the graph: parabola pass (0,4) (3,4) (1,2)
equation: y = ax² + bx + c
(0,4): c = 4
(3,4): 9a + 3b + 4 = 4 9a+3b = 0 3a + b = 0 ... (1)
(1,2): a + b + 4 = 2 a+b = -2 ... (2)
(1)-(2): 2a = 2 a = 1
(2): b = -3
parabola equation: f(x) = x² - 3x +4
(a) f(3) = 3² - 3*3 + 4 = 4
(b) normal line: parallel to tangent line y = 3x -5 at (3,4)
slope of line N: -1/3 pass (3,4)
equation of N: (y-4)/(x-3) = -1/3 y-4 = -1/3 x + 1
line N: 1/3 x + y - 5 = 0
(c) picture attached
