To generate points for the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), you can choose various values for \( x \) and calculate the corresponding \( y \) values. Here are a few points:
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Let \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \] Point: \( (0, 8) \)
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Let \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \] Point: \( (1, 5) \)
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Let \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \] Point: \( (-1, -1) \)
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Let \( x = 2 \): \[ y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \] Point: \( (2, -10) \)
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Let \( x = -2 \): \[ y = -6(-2)^2 + 3(-2) + 8 = -24 - 6 + 8 = -22 \] Point: \( (-2, -22) \)
These points, such as \( (0, 8) \), \( (1, 5) \), \( (-1, -1) \), \( (2, -10) \), and \( (-2, -22) \), can all be used to plot the parabola defined by the given quadratic equation.
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