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
Here are the completed tables for the given equations: c) For the equation y = x^2 - 3: Step 1: Substitute each x value into the equation to find the corresponding y value. For x = -3: y = (-3)^2 - 3 = 9 - 3 = 6 For x = -1: y = (-1)^2 - 3 = 1 - 3 = -2 For x = 0: y = (0)^2 - 3 = 0 - 3 = -3 For x = 2: y = (2)^2 - 3 = 4 - 3 = 1 For x = 4: y = (4)^2 - 3 = 16 - 3 = 13 The completed table is: |c|c|c|c|c|c| x & -3 & -1 & 0 & 2 & 4 \\ y & 6 & -2 & -3 & 1 & 13 \\ d) For the equation y = x^2 - 5: Step 1: Substitute each x value into the equation to find the corresponding y value. (Assuming the missing x values are 1 and 3 to complete the table pattern.) For x = -4: y = (-4)^2 - 5 = 16 - 5 = 11 For x = -1: y = (-1)^2 - 5 = 1 - 5 = -4 For x = 0: y = (0)^2 - 5 = 0 - 5 = -5 For x = 1: y = (1)^2 - 5 = 1 - 5 = -4 For x = 3: y = (3)^2 - 5 = 9 - 5 = 4 The completed table is: |c|c|c|c|c|c| x & -4 & -1 & 0 & 1 & 3 \\ y & 11 & -4 & -5 & -4 & 4 \\ e) For the equation y = 2x^2 + 1: Step 1: Substitute each x value into the equation to find the corresponding y value. For x = -6: y = 2(-6)^2 + 1 = 2(36) + 1 = 72 + 1 = 73 For x = -5: y = 2(-5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51 For x = 0: y = 2(0)^2 + 1 = 0 + 1 = 1 For x = 5: y = 2(5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51 For x = 6: y = 2(6)^2 + 1 = 2(36) + 1 = 72 + 1 = 73 The completed table is: |c|c|c|c|c|c| x & -6 & -5 & 0 & 5 & 6 \\ y & 73 & 51 & 1 & 51 & 73 \\ f) For the equation y = 2x^2 - 1: Step 1: Substitute each x value into the equation to find the corresponding y value. (Assuming the missing x values are 1 and 2 to complete the table pattern.) For x = -2: y = 2(-2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7 For x = -1: y = 2(-1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1 For x = 0: y = 2(0)^2 - 1 = 0 - 1 = -1 For x = 1: y = 2(1)^2 - 1 = 2(1) - 1 = 2 - 1 = 1 For x = 2: y = 2(2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7 The completed table is: |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & 7 & 1 & -1 & 1 & 7 \\ Got more? Send 'em!