To determine which of the points can be generated to create the parabola for the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute each point into the equation and see if it satisfies the equation (i.e., if the left-hand side equals the right-hand side).
Let's check each point:
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For \((-6, 206)\): \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 = -226 \quad \text{(not } 206\text{)} \]
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For \((-3, -55)\): \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 = -55 \quad \text{(this point works)} \]
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For \((-6, 8)\): \[ y = -6(-6)^2 + 3(-6) + 8 \] This calculation is the same as the first point, which we already evaluated to be: \[ = -226 \quad \text{(not } 8\text{)} \]
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For \((-3, 323)\): \[ y = -6(-3)^2 + 3(-3) + 8 \] As we calculated before, this gives us: \[ = -55 \quad \text{(not } 323\text{)} \]
The only point that satisfies the equation \( y = -6x^2 + 3x + 8 \) is \((-3, -55)\).
Thus, the correct response is: \((-3, -55)\).
1 answer