To generate points for the parabola of the quadratic equation \( y = -6x^2 + 3x + 8 \), you can choose various values for \( x \) and then calculate the corresponding \( y \) values using the equation.
Here are a few example points:
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For \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \quad \Rightarrow \quad (0, 8) \]
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For \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \quad \Rightarrow \quad (1, 5) \]
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For \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \quad \Rightarrow \quad (-1, -1) \]
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For \( x = 2 \): \[ y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \quad \Rightarrow \quad (2, -10) \]
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For \( x = -2 \): \[ y = -6(-2)^2 + 3(-2) + 8 = -24 - 6 + 8 = -22 \quad \Rightarrow \quad (-2, -22) \]
Thus, some points you can generate to create the parabola are:
- \( (0, 8) \)
- \( (1, 5) \)
- \( (-1, -1) \)
- \( (2, -10) \)
- \( (-2, -22) \)
These points can help you graph the parabola.
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