To generate points to create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), you can choose different values for \( x \) and calculate the corresponding \( y \) values. Here are a few values of \( x \) and their corresponding \( y \):
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When \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \quad \text{(Point: (0, 8))} \]
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When \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \quad \text{(Point: (1, 5))} \]
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When \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \quad \text{(Point: (-1, -1))} \]
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When \( x = 2 \): \[ y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \quad \text{(Point: (2, -10))} \]
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When \( x = -2 \): \[ y = -6(-2)^2 + 3(-2) + 8 = -24 - 6 + 8 = -22 \quad \text{(Point: (-2, -22))} \]
You can continue to calculate more points to get a better graph of the parabola. The points generated above include:
- (0, 8)
- (1, 5)
- (-1, -1)
- (2, -10)
- (-2, -22)
These points should help in plotting the parabola defined by the quadratic equation.
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