Question

10 For the given equation and graph of the quadratic function, do each of the following. Complete parts (a) through (e). f(x) = -2(x - 5y2 + 2 a. Give the domain and range. The domain is (Type your answer in interval notation.) The range is (Type your answer in interval notation.) M h -10-8-82 2 -4 -6 -B 10 b. Give the coordinates of the vertex. The vertex is (Type an ordered pair.) c. Give the equation of the axis of symmetry The axis of symmetry is - d. Find the y-intercept(s). The y-intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) e. Find the x-intercept(s). The x-intercept(s) is/are 0 Tin nn naninirlenmmnnnt un nodod Enter your answer in each of the answer boxes.

Answer 1

f(x) = -2 (M-5)+a (a) Domain: The domain of a polynomial function is the set of all real numbers. Since, feu) is a polynomial so, the domain is HER Range : . The range of the function is same as the domain of inverse function. Now, Inverse of function f(x) - het fra)=y n=f(y) y=-2 (2-5) 78 => x6 (-00,00) (9-2) = -2(x-5) y-21 U-S ܐ - 2-Y =u 5+2= 5 t +1 2-4 f-'(y) 2 st 12-1 2-4 f'(X) { swap noy} The domain of f'(x) is 2-0 20 -) 237 -) 719 ne (-0,2 so domain of f'(X) = range of f(x) 2166-00,2 (b) vertin =) (5,2) (from Equation (C) f(a) -9(0-5) +2 5-22+02-24 Anis of Symmetry (*) = -6 -(10) a=-1 b=10, c=-24 1 = 5 -) 3-5 za 261) y = f(0) = =48=y y (a) y-intercept =) Put x=0 2 (0-5)²+2 -2(25)+2 (e) a-intercept =) Put Y=0 Yo - f(x) = 0 = -262-5)2+2 O = -(04-5)2+1 (21-5) 2 =) #1 = 3-5 TEN-5 =) 4-6 -1-2-5 =) x=4 Answer