Given the graph of y = 2x2 - x - 1, solve 2x2 - 3x - 3 = 0 and 2x2 - 2x - 1 = 0 using suitable straight lines.

The image provided is very blurry, making it difficult to read all the questions clearly. I will solve the graphing problem, specifically parts (b) and (c), as part (a) requires drawing a graph which cannot be done here. I will assume this is Question 20 based on the previous questions. Question 20: Given the graph of y = 2x^2 - x - 1. b) Using a suitable straight line, solve 2x^2 - 3x - 3 = 0. c) Using a suitable straight line, solve 2x^2 - 2x - 1 = 0. --- b) Solve 2x^2 - 3x - 3 = 0 using the graph of y = 2x^2 - x - 1. Step 1: Identify the given graph equation and the equation to be solved. Given graph: y = 2x^2 - x - 1 Equation to solve: 2x^2 - 3x - 3 = 0 Step 2: Manipulate the equation to be solved to relate it to the given graph equation. We want to express 2x^2 - 3x - 3 = 0 in terms of y = 2x^2 - x - 1. Rewrite 2x^2 - 3x - 3 = 0 as: (2x^2 - x - 1) - 2x - 2 = 0 Substitute y for (2x^2 - x - 1): y - 2x - 2 = 0 y = 2x + 2 This is the equation of the suitable straight line. Step 3: Explain the graphical solution. To solve 2x^2 - 3x - 3 = 0 graphically, you would draw the straight line y = 2x + 2 on the same axes as the graph of y = 2x^2 - x - 1. The solutions for x are the x-coordinates of the points where the straight line intersects the parabola. Step 4: Solve the equation algebraically to find the exact values (as a graph would provide approximations). Using the quadratic formula x = -b ± sqrt(b^2 - 4ac)2a for 2x^2 - 3x - 3 = 0 (where a=2, b=-3, c=-3): x = -(-3) ± sqrt((-3)^2 - 4(2)(-3))2(2) x = 3 ± sqrt(9 + 24)4 x = 3 ± sqrt(33)4 The solutions are x = 3 + sqrt(33)4 and x = 3 - sqrt(33)4. Approximately, x ≈ (3 + 5.745)/(4) ≈ 2.186 and x ≈ (3 - 5.745)/(4) ≈ -0.686. The suitable straight line is y = 2x + 2. The solutions are x = 3 ± sqrt(33)4. --- c) Solve 2x^2 - 2x - 1 = 0 using the graph of y = 2x^2 - x - 1. Step 1: Identify the given graph equation and the equation to be solved. Given graph: y = 2x^2 - x - 1 Equation to solve: 2x^2 - 2x - 1 = 0 Step 2: Manipulate the