To generate points that create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), you can substitute various values of \( x \) into the equation to calculate the corresponding values of \( y \).
Here are a few examples of points you can generate:
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For \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \] So, the point is \( (0, 8) \).
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For \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \] So, the point is \( (1, 5) \).
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For \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6 - 3 + 8 = -1 \] So, the point is \( (-1, -1) \).
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For \( x = 2 \): \[ y = -6(2)^2 + 3(2) + 8 = -24 + 6 + 8 = -10 \] So, the point is \( (2, -10) \).
These calculations show how to generate points, and any of these points can be used to plot the parabola defined by the given quadratic equation.
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