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
To plot the points for the equation y = x^2 + 4x - 10 on the graph paper, follow these steps: Step 1: Set up the axes and scale. Draw a horizontal x-axis and a vertical y-axis. A suitable scale for the given values would be: • On the x-axis: Let 1 major grid square represent 1 unit. • On the y-axis: Let 1 major grid square represent 2 units. Place the origin (0,0) near the center of the graph paper to accommodate both positive and negative values. Step 2: Plot each point using the chosen scale. Locate each coordinate pair (x, y) on the graph paper: • For (-4, -10): Move 4 major squares left from the origin, then 5 major squares down (since 10 units / 2 units/major square = 5 major squares). • For (-3, -13): Move 3 major squares left from the origin, then 6.5 major squares down (since 13 units / 2 units/major square = 6.5 major squares). This is 6 major squares and 5 small squares down. • For (-2, -14): Move 2 major squares left from the origin, then 7 major squares down (since 14 units / 2 units/major square = 7 major squares). • For (-1, -13): Move 1 major square left from the origin, then 6.5 major squares down. • For (0, -10): Stay on the y-axis, then move 5 major squares down from the origin. • For (1, -5): Move 1 major square right from the origin, then 2.5 major squares down (since 5 units / 2 units/major square = 2.5 major squares). This is 2 major squares and 5 small squares down. • For (2, 2): Move 2 major squares right from the origin, then 1 major square up (since 2 units / 2 units/major square = 1 major square). • For (3, 11): Move 3 major squares right from the origin, then 5.5 major squares up (since 11 units / 2 units/major square = 5.5 major squares). This is 5 major squares and 5 small squares up. Step 3: Draw the curve. Once all points are plotted, draw a smooth curve connecting them. The graph should form a parabola opening upwards. The points to plot are: (-4, -10), (-3, -13), (-2, -14), (-1, -13), (0, -10), (1, -5), (2, 2), (3, 11) That's 2 down. 3 left today — send the next one.