Question

Hi, can anyone help with b) and c)?

Answer 1

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