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Use this for an instance to solve the equation I gave earlier show each points

Mathematics

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3 steps

To plot the points for the equation y=x2+4x−10y = x^2 + 4x - 10 on the graph paper, follow these steps:

  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.
  2. Plot each point using the chosen scale.

    Locate each coordinate pair (x,y)(x, y) on the graph paper:

    • For (−4,−10)(-4, -10): Move 4 major squares left from the origin, then 5 major squares down (since 10 units/2 units/major square=5 major squares10 \text{ units} / 2 \text{ units/major square} = 5 \text{ major squares}).
    • For (−3,−13)(-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 squares13 \text{ units} / 2 \text{ units/major square} = 6.5 \text{ major squares}). This is 6 major squares and 5 small squares down.
    • For (−2,−14)(-2, -14): Move 2 major squares left from the origin, then 7 major squares down (since 14 units/2 units/major square=7 major squares14 \text{ units} / 2 \text{ units/major square} = 7 \text{ major squares}).
    • For (−1,−13)(-1, -13): Move 1 major square left from the origin, then 6.5 major squares down.
    • For (0,−10)(0, -10): Stay on the y-axis, then move 5 major squares down from the origin.
    • For (1,−5)(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 squares5 \text{ units} / 2 \text{ units/major square} = 2.5 \text{ major squares}). This is 2 major squares and 5 small squares down.
    • For (2,2)(2, 2): Move 2 major squares right from the origin, then 1 major square up (since 2 units/2 units/major square=1 major square2 \text{ units} / 2 \text{ units/major square} = 1 \text{ major square}).
    • For (3,11)(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 squares11 \text{ units} / 2 \text{ units/major square} = 5.5 \text{ major squares}). This is 5 major squares and 5 small squares up.
  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)\boxed{ (-4, -10), (-3, -13), (-2, -14), (-1, -13), (0, -10), (1, -5), (2, 2), (3, 11) }
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