Question

Show all steps clearly, to receive full marks for your solutions. Use the discriminant to determine the number of x-intercepts for each quadratic function: .ft) = 3x - 5x+ f = 2x +x+1 f(x) = 4x - 12x + 9 16 marks) 15. Express the function f(x) = 47° - 12x + 5 in factored form and determine the -intercepts and the vertex Sketch the graph of the function. State the minimum or maximum value. (9 marks) 16 Express the function () 5 + 20% - 2 in vertex form

please answer ALL questions.

Answer 1

f(x) = 2x24x+1 b²-fac 14: )-3-4-5+1 discriminant - b²-4ac. b7-erc=0(1realsociation) b? Anc 70 12 real solution) b2-44C2012 nonreal solutions) Here a 3 b= -5 cal (-5)-4X3X1 25-12 a=2 b=1 call 1092-4X2X1 1-8 =-7. 6²-40cco : 2 noreal x-intercepts - 13 I real x-interceptul f(x) = 4222-19279. a:4 6: -12 6:9 be fac (-1292-4x4x9 144-144 bf-4ac=0 .i I real X-intercept

factoredfom. 16. fby - 4x2-12245 471-101-2215 432-2X-10X45 22[22-13-5122-1) (24-5)/22=1 있은 equate to o 122C-5) (22-1)=0 X=8=142 13:01:{4:02 -intercefta. vertex of up-down facing parabola of y=an² batc is ob .: Here. a=4 b=-12 (=5 -(-12) 4= 4(2) - 12254)+5) 9-18+5 = -4 29. = 12 = 3 2 2x4 .. vertex = (361-4)

graph Mand 157) -4 18/2-4 since aro vertex is a méninul value .. Minimum (3-4)

16 unknown. fl4] =-58%+20X+2 81+4= -5(4-4473) +2. Yf4--564-4674) 4+254) = -513°- 44+4) +2 (Adding. 20.on both sides -514-2) +2. 4-20 Y: -5(4-2)+22) & vertexform Vertex =-b Here a=-5 b=20 (=2 2a K: -20 -2 26-59 -10 y-5(2)2+2062)+2 = -20+40+2 = 22 fuestes (222) since Here aloi.e-520 vertex is Maximumvalue ise (2,227) f() --5X2+2014+2. equratiyong to Ogives x-intercefoto -5427202+2=0 : -207 120746-592 ~10+ 500 24-5) .: L-intercepts are 4-10+ $110)