Question

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3. Find the coordinates of the vertex, the axis of symmetry, the intervals the graph is increasing and decreasing respectively, the domain and the range of the following quadratic functions: (a) f(0) = 22 +2 (b) g(x) = 2x2 – 8x + 7 (c) h(x) = -3x2 + 9x +7 (d) p(x) = 3x2 – 7x – 5 (e) q(x) = -13x2 + 14x + 15 4. Find all solutions to the following equations and inequalities: (a) 2x + 3) = 5 (b) 3.x – 5= 2 (C) 15+ 8= -1 (d) (x – 4[<2 (e) 2 - 6 <3 (f) 2x - 3| > 1 (g) (3x – 11 <-3 (h) 2 + 4 > -7

Answer 1

(a) / 2x+315 12x+31252 Isinaning both side we get / = (2x + 3)2 = 25 - 4x² + 12 x + 9 = 25 { using (ath) ² a ² + 2ab +62] => 4x²+120-16=0 x² + 3x -4 = 0 re² - 4x +X-450 recx-4)+(2-4)=0 = (-4)(x+1)=0 x=+4,-1 (b) 3x-51 = 2 > 134-51² = 4 (38-5) 2 = 4 >> 942-30x+25= 4 3 9x² 30x+21=0 souls » 3 x²_lox+7=0 => 3 x2_72-3x+7=0 > (36-7)-(3x-7)=0 (3x-7)(2-1)=0 (e) 15*+81 =-1 => 15x+81 (-12 -> (5x+8 ) ² = 1 - 25 x ² + 80 x + 64 = 1 > 25*² + 80x+63=0 > 25x²+45x+350 +63=0 - 5+(5x+7)+9 (5x+7)=0 (5x+7) (5x+9)=0

=> arra - 2 < x-4 <2 3 - 2+4 < x-4+4 L2+4 → 2 < x < 6 - 1 x-61 <3 - 3 < x-6 L3 - 3 +6 <r < 3 +6 => 3 < x 29 (4) 12x- 311, [12lxa => xa and a la - 2x-3 >1 7 2 > 1+3 => 2474 => x 2 and 28-3 <1 => 2131+3 - 2x 2 - 3. (8) 13x-1| 2-3 Absolute of 3*-1 can not be less than so there is no solution. ch) 1 x +41-7 = x+47-7 and x+4 247 x +4-47-7-4 7x+4-4 <7-4 7 x>-11 => x <3