To fill in the missing y-values for the given x-values in the equation of the parabola \( y = -18x^2 + 34x + 78 \), we can calculate the y-value for each x-value provided.
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For \( x = -1 \): \[ y = -18(-1)^2 + 34(-1) + 78 = -18(1) - 34 + 78 = -18 - 34 + 78 = 26 \]
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For \( x = 0 \): \[ y = -18(0)^2 + 34(0) + 78 = 0 + 0 + 78 = 78 \]
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For \( x = 3 \): \[ y = -18(3)^2 + 34(3) + 78 = -18(9) + 102 + 78 = -162 + 102 + 78 = 18 \]
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For \( x = 2 \): \[ y = -18(2)^2 + 34(2) + 78 = -18(4) + 68 + 78 = -72 + 68 + 78 = 74 \]
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For \( x = 11 \): \[ y = -18(11)^2 + 34(11) + 78 = -18(121) + 374 + 78 = -2178 + 374 + 78 = -1726 \]
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For \( x = -6 \): \[ y = -18(-6)^2 + 34(-6) + 78 = -18(36) - 204 + 78 = -648 - 204 + 78 = -774 \]
Now, we compile the results:
| x-value | y-value | |---------|---------| | -1 | 26 | | 0 | 78 | | 3 | 18 | | 2 | 74 | | 11 | -1726 | | -6 | -774 |
The missing values for the table are:
- For \( x = -1, \) the \( y-value = 26 \)
- For \( x = 0, \) the \( y-value = 78 \)
- For \( x = 3, \) the \( y-value = 18 \)
- For \( x = 2, \) the \( y-value = 74 \)
- For \( x = 11, \) the \( y-value = -1726 \)
- For \( x = -6, \) the \( y-value = -774 \)