To trace the curve represented by the equation y = 2x^3 - 6x + 1, you can create a table of values and plot some points on a graph to visualize the curve. Here's a set of x and y values to get you started:
- When x = -2:
y = 2(-2)^3 - 6(-2) + 1 = -16 + 12 + 1 = -3
- When x = -1:
y = 2(-1)^3 - 6(-1) + 1 = -2 + 6 + 1 = 5
- When x = 0:
y = 2(0)^3 - 6(0) + 1 = 0 - 0 + 1 = 1
- When x = 1:
y = 2(1)^3 - 6(1) + 1 = 2 - 6 + 1 = -3
- When x = 2:
y = 2(2)^3 - 6(2) + 1 = 16 - 12 + 1 = 5
You can plot these points on a graph, and you'll see a curve that passes through these points. This curve represents the equation y = 2x^3 - 6x + 1.
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Answer:
To trace the curve represented by the equation y = 2x^3 - 6x + 1, you can create a table of values and plot some points on a graph to visualize the curve. Here's a set of x and y values to get you started:
- When x = -2:
y = 2(-2)^3 - 6(-2) + 1 = -16 + 12 + 1 = -3
- When x = -1:
y = 2(-1)^3 - 6(-1) + 1 = -2 + 6 + 1 = 5
- When x = 0:
y = 2(0)^3 - 6(0) + 1 = 0 - 0 + 1 = 1
- When x = 1:
y = 2(1)^3 - 6(1) + 1 = 2 - 6 + 1 = -3
- When x = 2:
y = 2(2)^3 - 6(2) + 1 = 16 - 12 + 1 = 5
You can plot these points on a graph, and you'll see a curve that passes through these points. This curve represents the equation y = 2x^3 - 6x + 1.