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
a) To complete the table, substitute each value of x into the equation y = 7 + 3x - x^2. For x = -2: y = 7 + 3(-2) - (-2)^2 = 7 - 6 - 4 = -3 For x = -1: y = 7 + 3(-1) - (-1)^2 = 7 - 3 - 1 = 3 For x = 2: y = 7 + 3(2) - (2)^2 = 7 + 6 - 4 = 9 For x = 3: y = 7 + 3(3) - (3)^2 = 7 + 9 - 9 = 7 For x = 4: y = 7 + 3(4) - (4)^2 = 7 + 12 - 16 = 3 For x = 5: y = 7 + 3(5) - (5)^2 = 7 + 15 - 25 = -3 The completed table is: |c|c|c|c|c|c|c|c|c|c|c| x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ y & -11 & -3 & 3 & 7 & 9 & 9 & 7 & 3 & -3 & -11 \\ b) To draw the graph of y = 7 + 3x - x^2: 1. Draw and label the x-axis and y-axis on the provided grid. 2. Choose a suitable scale for both axes. For example, 1 cm to represent 1 unit on the x-axis and 1 cm to represent 2 units on the y-axis. Ensure the scale accommodates x-values from -3 to 6 and y-values from -11 to 9. 3. Plot the points from the completed table: (-3, -11), (-2, -3), (-1, 3), (0, 7), (1, 9), (2, 9), (3, 7), (4, 3), (5, -3), (6, -11). 4. Draw a smooth curve connecting all the plotted points. This curve will be a parabola opening downwards.