This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Complete Table 1 for y = x^2 - 3x - 4 For x = -1 : y = (-1)^2 - 3(-1) - 4 y = 1 + 3 - 4 y = 0 For x = 0 : y = (0)^2 - 3(0) - 4 y = 0 - 0 - 4 y = -4 For x = 1 : y = (1)^2 - 3(1) - 4 y = 1 - 3 - 4 y = -6 For x = 2 : y = (2)^2 - 3(2) - 4 y = 4 - 6 - 4 y = -6 For x = 3 : y = (3)^2 - 3(3) - 4 y = 9 - 9 - 4 y = -4 Completed table: c|c|c|c|c|c x & -1 & 0 & 1 & 2 & 3 \\ y & 0 & -4 & -6 & -6 & -4 \\ Step 2: Draw the graph Use the scale: 1 cm represents 1 unit on the x-axis and 1 cm represents 1 unit on the y-axis. Plot points: (-1, 0), (0, -4), (1, -6), (2, -6), (3, -4). Join with a smooth curve. The graph is a parabola opening upwards (vertex near (1.5, -6.25)). Step 3: Use graph to solve x^2 - 3x - 4 = 0 The graph crosses y = 0 at x = -1 (exact) and at x = 4 (by extending the curve beyond x = 3). Solutions: x = -1,\ 4 x = -1,\ 4