Question

answer all and show work please. clear hand writing please

1. (6 points) Let f(x) = -x2 - 2x + 3. (a) Does the graph of f(x) open upward or downward? Justify your answer. 6) Algebraically find the vertex and axis of symmetry of f(x). Report each answer as an ordered pair and equation, respectively, Vertex Axis of Symmetry: (C) Algebraically find the X- and y-intercepts of f(x). Report your answer(s) as an ordered pair(s). x-intercepts: y-intercept: (a) Using parts (a) - (d), graph /G) on the axes provided. Clearly indicate key points (including a point of symmetry) and sketch the axis of symmetry,

Answer 1

C-a ✓ f(a) re² 2x+3 - art batc -> a=-1, 6-2, 6-3 Here a=1<0 then f(x) opery downward. b -b 2a =-1 x=co-ordinate of vertes = 26-12 put x=- in fixe) f(-1)=-(-17²-2(-1) +3=-1+2+3=4 Y-coordinate of verter is .. verten = (-1,4) x = -b 20 ie. x=-1 Axis of symmetry: =-) To find x-intersept, put y=0 i-e- fx) zo 1 0= -x-2x+3 a (x2+2x)+3 A ge²722-3=0 - 3+336-1.26-350 = a (x+3) -1 (2+3)=0 (0+3)(02-1220 x=-3 f2=1. x intercepts are: 86=-3 f 801 To find y-intercept: put azo in foc) f(0) =-02-2(0)+3=3 Y-intercept :3

d 2001 n (-1,45 h 363,0) 1 (1,0) f x -3.2a 0 -s-h 7 f 2 3 ks al (43,0) 1-2 3