To generate points for the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), you can choose various values for \( x \) and calculate corresponding \( y \) values. Here are a few points generated from that equation:
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If \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \] So the point is \( (0, 8) \).
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If \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \] So the point is \( (1, 5) \).
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If \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \] So the point is \( (-1, -1) \).
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If \( x = 2 \): \[ y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \] So the point is \( (2, -10) \).
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If \( x = -2 \): \[ y = -6(-2)^2 + 3(-2) + 8 = -24 - 6 + 8 = -22 \] So the point is \( (-2, -22) \).
Any of these points can be used to help sketch the parabola. For instance, \( (0, 8) \), \( (1, 5) \), \( (-1, -1) \), \( (2, -10) \), or \( (-2, -22) \) are all points on the parabola described by the equation \( y = -6x^2 + 3x + 8 \).