Answer all questions correctly

1. Quadratic expressions and equation 2 1. Complete the table below for the function y =2x3 +5x2 -x-6 (2 mks) -4 -3 -2 -1 0 2 2x -128 0 16 80 45 20 20 -x 0 -1 -6 (b) On the grid provided draw the graph y = 2x +5x3 -x-6for-4x$ 2. Use 2cm to represent 1 unit on the x-axis and 1 cm to represent 5 units on the y - axis (4 mks) (c) By drawing a suitable line, use the graph in (b) to solve the i. equation 2x3 +5x2 +x-4=0 (2 mks) ii. equation 2x' + 5x' - x+2=0 (2 mks) 2. The curve y = 2x -6x +9 passes through the point P(2, 5) (a) Determine the gradient function of the curve (1 mk) (b) Determine the coordinates and nature of the turning point of the curve (5mks) (c) Find the equation in the form y = mx +cof the (i) Tangent to the curve at P (2mks) (ii) Normal to the curve at P (2mks) 3. The sketch below represents the graph of y = x - x - 6. Use the curve and five trapezia to estimate the area bounded by the x - axis, y - axis and the line x = 5. (3mks) 4. Draw the graph of y = 2x2 + x - 2 and use it to solve the equations (10 marks) a) 2x- + x - 2 =5 b)2x-+ x -5=0 c)2x2 +2x - 3 =0 5. Plot a graph of y = 2x2+ 3x - 5, -4 x 2 by completing the table below. X -4 -3 -2 -1 0 1 2 2x2 -18 0 3x - 12 -3 6 y -3 0 Use your graph to solve (i) 2x2 + 3x - 5 = 0 (ii) 2x2 + 6x - 2 = 0 6. Given the equation of a quadratic curve y = x~ + 5x - 3 (a) (i) Complete the table below for the function y = x + 5x - 3 for -6 5 x $ 1 -6 -5 -4 -3 y -3 -2 10 1-3 (2mks) (ii) Draw the graph of y = x* + 5x - 3 for -6 S x $ 1 (3mks) (b) (i) State the equation of the line of symmetry for the graph (1mk) (ii) Use the graph you have drawn to solve the equations; x- + 5x - 3=0 (1mk) x~ + 4x - 2=0 (2mks) x + 5x - 3 =-3 (2mks) 7. (a) Draw the graph of y = 2x2 - x-3 for -3 Sx53 (5 marks) (b) Using a suitable line solve 2x - 3x - 50 = 0 (5 marks) 8. (a) Draw the graph of y = x- + 4x + 1 for -4 x 2. (Show the table of values) (b) On the same axis, draw line y = 3x + 2. (c) Use the graph to solve the equations (i) x + 4x +1 =0 (ii) x + x -1=0 a) Draw the graph of the equation y = x'- 9x for - 4 S x 54 b) Use your graph to solve the following equations i) x' = 9x ii) y-5=0 iii) 0=x - 13x - 12 (10 Mks)